Melissa Aldana was born on December 3, 1988, in Santiago, Chile, the daughter of the tenor saxophonist and teacher Marcos Aldana. She began asking her father for lessons at six, and he started her on alto saxophone, teaching largely by having her transcribe solos from cassettes; the first player she learned from was Charlie Parker. Hearing Sonny Rollins changed her direction and she switched to tenor, playing a Selmer Mark VI that had belonged to her grandfather Enrique, who had taught her father. By sixteen she was headlining clubs in Santiago.

When the pianist Danilo Pérez came to Chile in 2005 as a member of Wayne Shorter's quartet, she made a point of meeting him; he invited her to the Panama Jazz Festival and then helped arrange American college auditions. She took a scholarship to Berklee College of Music in Boston, where her teachers included Joe Lovano, George Garzone, Greg Osby, Hal Crook, Bill Pierce and Ralph Peterson. After graduating in 2009 she moved to New York City and studied with George Coleman. Her debut as a leader, Free Fall (2010), came out on Osby's Inner Circle Music label, followed by Second Cycle (2012), a trio date with bassist Joseph Lepore and drummer Ross Pederson that adds trumpeter Gordon Au on several tracks.

In 2012 she formed Melissa Aldana & Crash Trio with the Cuban drummer Francisco Mela and the Chilean bassist Pablo Menares, whom she had known from the Santiago scene. In 2013, at 24, she won the Thelonious Monk International Jazz Saxophone Competition, becoming the first woman, the first South American and the youngest winner; her father had been a semifinalist in 1991. The jury included Jane Ira Bloom, Branford Marsalis, Jimmy Heath, Shorter and Bobby Watson, and the prize carried a $25,000 scholarship and a Concord Jazz recording contract. Melissa Aldana & Crash Trio appeared on Concord in July 2014; she played with Heath at the 2014 NEA Jazz Masters ceremony and was invited to Jazz at Lincoln Center by Wynton Marsalis. The trio's second album, Back Home (March 2016, Wommusic), replaced Mela with drummer Jochen Rückert.

Visions (2019, Motéma Music) was a quintet record inspired by the painter Frida Kahlo, with pianist Sam Harris, bassist Menares, drummer Tommy Crane and the vibraphonist Joel Ross; three of its pieces began as a suite commissioned by the Jazz Gallery, and the Slovenian tenor saxophonist Jure Pukl co-produced it. Her solo on "Elsewhere" earned a Grammy nomination for Best Improvised Jazz Solo. She was also the tenor saxophonist in Artemis, the all-women band led by pianist Renee Rosnes with trumpeter Ingrid Jensen, clarinetist Anat Cohen, bassist Noriko Ueda and drummer Allison Miller, on its self-titled 2020 Blue Note debut; Nicole Glover later took the tenor chair.

12 Stars (March 4, 2022) was her first album for Blue Note, made with guitarist Lage Lund (who co-produced), pianist Sullivan Fortner, Menares and drummer Kush Abadey, with Don Was as executive producer; its opening piece, "Falling," brought a second Grammy nomination for Best Improvised Jazz Solo. Echoes of the Inner Prophet (April 5, 2024) paired her with Lund, pianist Fabian Almazan, Menares and Abadey, and dedicated its title piece to Shorter. Filin (February 13, 2026), her third Blue Note album, is a ballads set drawn from Cuba's filin song tradition, played with pianist Gonzalo Rubalcaba (who wrote the arrangements), bassist Peter Washington and Abadey, with Cécile McLorin Salvant singing on two tracks and Was producing. On August 21, 2026 came Beneath Lifted Skies, a duo album of standards and free improvisations with the bassist Linda Oh, released on Biophilia Records. Her other honors include the Altazor National Arts Award of Chile, Lincoln Center's Martin E. Segal Award and a place on DownBeat's "25 for the Future" list in 2016.

Aldana is known for fluid, harmonically alert tenor lines rooted in the acoustic post-bop tradition. Her models are the tenor players she has long transcribed: Rollins, Shorter, John Coltrane, Joe Henderson, Lester Young, Parker and Don Byas, and as a teenage alto player she also listened to Cannonball Adderley and Michael Brecker. Her records stay close to the quartet or quintet format, with her own compositions placed alongside pieces by her bandmates and an occasional standard, and she has used each project to name a specific source: Kahlo for Visions, her mentors (Shorter above all) for Echoes of the Inner Prophet, and Coltrane's ballad records for Filin. A reviewer at PopMatters credited Visions with a sense of group interplay shaped by the personalities she picked for it, and The Washington Post's coverage of the 2013 Monk competition framed her win as a sign of a changing direction in jazz.