Hendrik Thomas Meurkens was born in Hamburg on August 6, 1957, to a Dutch father and a German mother whose record collection held both jazz and Brazilian music. He took piano lessons and played drums with friends before settling, at sixteen, on the vibraphone, which he chose because it seemed to him the best marriage between the two. He taught himself, working with two mallets in the manner of Lionel Hampton and Milt Jackson, and came to think of the instrument as a horn, "a saxophone with mallets." He studied with the German vibraphonist Wolfgang Schlüter in 1976 and 1977. At nineteen he heard Toots Thielemans play the chromatic harmonica and bought one the next day; entirely self-taught on it again, he has made it his primary instrument ever since.

He came to the United States in 1977 to attend the Berklee College of Music, where he spent three years as a vibraphone major while practising harmonica privately and transcribing Charlie Parker solos to play on it. Brazilian music had gripped him since his teens, and in 1982 he moved to Rio de Janeiro at the invitation of Maurício Einhorn, the Brazilian harmonica player and bossa nova composer, who put him up during his first days in the country. He took an apartment in Rio and held a regular Monday night gig at the club Bar 21, which is where he met most of the Brazilian musicians who would turn up on his records for the next four decades. He was back in Hamburg by 1983, the year he won first prize for jazz from the German Phono Academy, and spent the rest of the decade as a studio and jazz musician in Germany, recording with the Danish Radio Orchestra and other European radio big bands, writing for German television, and backing visiting Americans including Harry "Sweets" Edison and Buddy Tate. His earliest surviving recording predates all of that: a 1978 self-released album by the group Salt City Seven, on which he plays vibraphone and no harmonica at all.

He returned to Brazil in 1989 to record his first album as a leader, Samba Importado, released internationally the following year with the vibraphonist David Friedman as featured guest. The record changed his life through an accident of geography. Visiting his wife, who was studying at Berkeley in 1990, he found himself in a Bay Area record store, discovered that Concord Records was a BART ride away, walked into the office with his album and presented it to the label's founder Carl Jefferson, who signed him and arranged a working visa. Six Concord albums followed. Sambahia (1991), on the label's Picante imprint, brought in Paquito D'Rivera and Claudio Roditi. Clear of Clouds (1992) sat in the top five of the American jazz radio charts for most of that winter, and A View from Manhattan (1993), his first record made after he settled in New York, reached number three. October Colors (1995) carries "Night in the Afternoon," the piece he was commissioned to write for the film Dolores Claiborne and played on screen, and Poema Brasileiro (1996) put sixteen musicians around him, including Ivan Lins singing lead, Romero Lubambo on guitars and Vanderlei Pereira in one of the drum chairs.

After leaving Concord in the late 1990s he recorded prolifically for a series of smaller labels: a harmonica and piano duo record, Quiet Moments (Evidence, 1998); Dig This Samba! with the blind Brazilian pianist Manfredo Fest (Candid, 1998); Burnin' with the Herb Ellis Trio and When Lights Are Lowe with Mundell Lowe, both on Acoustic Music Records; In a Sentimental Mood (1999) and New York Nights (2000) for A-Records, the second of them putting Jimmy Cobb in the drum chair and Eric Alexander on four tracks; and Encontros: Meetings (2000), co-led with the bassist Nilson Matta, with Duduka Da Fonseca on drums. Amazon River (Blue Toucan, 2005), co-produced with Oscar Castro-Neves, was his first deliberate concept record, a survey of Brazilian styles from samba to chorinho scored for small group and strings, and he has called it the most complete statement of what he does.

From 2007 he settled into a long run on ZOHO Music, beginning with the live New York Samba Jazz Quintet and continuing through Sambatropolis (2008), Samba to Go! (2009) and Live at Bird's Eye (2011), the last three built around his working samba-jazz quartet with pianist Misha Tsiganov, bassist Gustavo Amarante and drummer Adriano Santos. Celebrando (2012), co-led with the Yucatecan bassist and singer Gabriel Espinosa, was ZOHO's hundredth CD release; Anat Cohen plays clarinet on three of its eleven pieces and tenor saxophone on a fourth, and Antonio Sanchez splits the drum chair with Mauricio Zottarelli. The same partnership reconvened almost the same band for Samba Little Samba (ZOHO, 2014). Since 2016 he has run his own label, Height Advantage, releasing Harmonicus Rex (2016) with Dado Moroni and Jimmy Cobb, the duo record Cabin in the Sky (2018) with Bill Cunliffe, and Manhattan Samba (2020). Cobb's Pocket (In+Out, 2019) is an organ quartet named for its drummer, with Mike LeDonne and Peter Bernstein, cut near the end of Cobb's career. Samba Jazz Odyssey (ZOHO, 2022) rescored his repertoire for the WDR Big Band Köln under Michael Philip Mossman, and two records for Cellar Music, The Jazz Meurkengers (2024) and Samba Tonto (2026), have carried the catalogue past thirty leader and co-leader titles. He has lived in New York since 1992.

Meurkens is the most widely recognised jazz chromatic harmonica player to emerge after Toots Thielemans, and the comparison follows him everywhere: one Canadian critic called him "the obvious leading player" on the instrument, and reviewers of the current generation of harmonica players, including the Israeli chromatic player Ariel Bart, reach reflexively for Thielemans first and Meurkens second. What distinguishes him is that he came to the harmonica from the vibraphone rather than from blues or folk traditions, and he plays it with a horn player's phrasing built on bebop vocabulary, which is what the Charlie Parker transcriptions at Berklee were for. On vibes he remains a two-mallet player in the Hampton and Jackson line. His Brazilian material is not a departure from that but the setting he prefers for it: he writes originals in samba, bossa and choro forms and plays them with a jazz improviser's harmonic language, a combination the Brazilian trumpeter Claudio Roditi described by saying that Meurkens's understanding of the Brazilian vocabulary is absolute and his writing feels like a native composer's. He composes sparingly and by his own account keeps a strict filter on what leaves the drawer, but his originals dominate his own records, typically five or six of every eight to eleven pieces. Jazziz readers placed him alongside Thielemans among the top harmonica players in the world in 1994, and the magazine's critics named Slidin' one of the best recordings of that year.