Yoni Zelnik came to music with no help from home. In a long 2007 interview with the French jazz site Les Dernières Nouvelles du Jazz, he described parents who owned no hi-fi and had no interest in music, a childhood spent partly in England, and a move to Israel at nine that left him isolated and friendless. School friends starting a rock band asked him to take the bass, and the social side of playing, more than the instrument itself, was what pulled him in. He found jazz two or three years later through a teacher who taught both electric bass and double bass, took him along to gigs, and lent him cassettes of the Miles Davis quintets. Miles Davis's Cookin' and Relaxin' were the records that decided him.

At eighteen he entered the jazz program at the music academy in Jerusalem, arriving with an electric bass, no improvising ability, and a walking line written out in a notebook for the entrance exam. He was the only bassist in a class of ten, which meant playing in every workshop. He has described a year of arriving at eight in the morning and leaving at nine at night, six days a week, and up to fourteen hours a day on the instrument. Within six months the electric bass had become intolerable to him: transcribing Paul Chambers solos on it made no sense, and he switched to double bass and never went back. Seven months of Israeli military service interrupted the work, he obtained a discharge, and three months later he left for France.

The move was practical as much as musical. His mother is French and he had grandparents in the country, and bassist Henri Texier, playing a concert in Israel, had pointed the family toward the CIM in Paris. His mother enrolled him there in 1995. The CIM was where he met the Korean singer Youn Sun Nah and the drummer David Georgelet, two of his longest-running musical relationships. Georgelet was the one organizing gigs in those first years, and both men were still in his working groups thirty years later. Zelnik joined Youn Sun Nah's quintet for Light For The People (2002) and So I Am..., cut February 2 to 4, 2004 at Studios La Buissonne in Pernes-les-Fontaines with pianist Benjamin Moussay and vibraphonist David Neerman, and played Jazz at Lincoln Center with the group in 2007. Alongside that he became a fixture of the Paris straight-ahead scene, recording with trumpeter Patrick Artero, saxophonist Sophie Alour, trumpeter Yoann Loustalot, guitarist Sandro Zerafa, and, from 2004, the Vintage Orchestra, a Paris big band devoted to the book of Thad Jones whose first album Thad came out that year on Nocturne.

The association that made his name in France began in 2005, when alto saxophonist Géraldine Laurent formed the Time Out Trio with Zelnik and drummer Laurent Bataille. Their album Time Out Trio appeared on Dreyfus Jazz in 2007, and Laurent took both the Prix Frank Ténot for French instrumental revelation at the 2008 Victoires du Jazz and the Académie du Jazz's Prix Django Reinhardt that same year. Zelnik stayed with her through every subsequent record: Around Gigi (2010, Dreyfus Jazz), a Gigi Gryce tribute with pianist Pierre de Bethmann and drummer Franck Agulhon; At Work, recorded in March 2015 at MidiLive Studios with pianist Paul Lay and drummer Donald Kontomanou, produced by Laurent de Wilde for Gazebo, which won the Académie Charles Cros Grand Prix du Jazz and the Académie du Jazz prize for best French record; and Cooking, cut March 18 to 20, 2019 and released October 18, 2019, which was named album of the year at the 2020 Victoires du Jazz. In 2023 the same quartet took the Victoires du Jazz awards for artist of the year and for touring.

The Kontomanou partnership carried into the other group Zelnik is best known for. Pianist Yonathan Avishai built his trio around the two of them and originally billed it as "Modern Times." Their first record under that name, Modern Times, was cut July 22 and 23, 2014 at Studio Juillaguet in the Charente and released March 10, 2015 on Jazz&People, sixteen tracks mixing Avishai originals with "I've Got It Bad (And That Ain't Good)" and Louis Armstrong's "Cornet Chop Suey." The Parade followed on November 18, 2016, recorded June 1 and 2 of that year at the Studio Gil Evans in Amiens with the trio expanded to a quintet by clarinettist and alto saxophonist César Poirier and percussionist Inor Sotolongo. Then came the ECM years: Joys and Solitudes, recorded at the Auditorio Stelio Molo RSI in Lugano in February 2018, produced by Manfred Eicher and issued January 25, 2019 as ECM 2611, and Shapes & Sounds, recorded March 31 to April 2, 2024 at Studio Sextan in Malakoff and released that October back on Jazz&People. Zelnik and Kontomanou are the bass and drums on all three trio albums plus the quintet date. Zelnik also spent 2016 on the road in trumpeter Avishai Cohen's quartet behind Into the Silence, with Avishai at the piano, playing Berlin's Gretchen on March 8 and Rotterdam's LantarenVenster on March 11 of that year, and has appeared with Cohen's Triveni.

He has led or co-led only a handful of records, by choice. Lucky Dog, cut December 12 to 14, 2013 at Studio Barge in Vannes and released on Fresh Sound New Talent in 2014, is a co-billed collective quartet with tenor saxophonist Frédéric Borey, trumpeter Yoann Loustalot and drummer Frédéric Pasqua; the same band issued Live At The Jacques Pelzer Jazz Club in 2018. Since 2012 he has also co-led a piano trio with David Georgelet and pianist François Chesnel, documented on three hand-numbered hundred-copy runs for the French label Petit Label: The Wee Small Hours (recorded December 20, 2012, released 2014), La Septième Reine (recorded April 11, 2022, released December 17, 2022) and Live For Gil (recorded March 24, 2025 in Caen with trombonist Thierry Lhiver, released January 29, 2026). The rest of his catalog is sideman work, and there is a great deal of it: Discogs credits him on 74 releases between 2000 and 2026, including four albums with pianist Leïla Olivesi, Fabien Mary's Vintage Orchestra, guitarist Romain Pilon's trio with Ben Wendel and Walter Smith III, saxophonist Shauli Einav's Animi, and the Laurent Coq Trio's Confidences. His own label biography puts the figure at over a hundred albums, in more than sixty countries, with appearances at the North Sea Jazz Festival, Jazz à Marciac, Jazz à Vienne and the Tokyo Jazz Festival.

Zelnik plays entirely acoustic, with no amplification at all, having abandoned the electric bass outright after his first months in Jerusalem. He has said plainly that he does not belong to the Scott LaFaro school of bass playing and describes himself instead as "beaucoup plus terrien," more earthbound: when he plays he listens to the drummer first and the soloist second, and he treats rhythmic coherence with the drums as the foundation everything else rests on. That preference shows in his working relationships, which are almost all long partnerships with specific drummers, Donald Kontomanou, David Georgelet, Laurent Bataille, Frédéric Pasqua. Reviewing the Georgelet/Zelnik/Chesnel trio in 2014, the French critic Nicolas Béniès called him a "maître du temps," a master of time, while keeping a round tone and intact musicality. He is equally frank about not wanting the front of the stage: he told an interviewer in 2007 that a bassist will never be a star in jazz, that this suits his character, and that a record under his own name would foreground the music rather than the instrument. What he listens for in other players is group thinking, and the bassists he names as ideals are Larry Grenadier and Drew Gress, with Mark Turner, Jason Moran and Chris Cheek among the leaders whose spirit he admires.