Marta Sánchez was born in Madrid, Spain, and originally studied filmmaking before discovering jazz and changing course. She earned a bachelor's degree in classical music from the Conservatory of Madrid, then continued with jazz and contemporary music studies at the School of Music Populart, receiving grant support from Spain's A.I.E. musicians' association that funded festival appearances across Spain, South America, Central America, and elsewhere in Europe. She won first prize at the Jazzargia International Jazz Contest as a member of the Javier Moreno Trio and first prize at the San Martín de la Vega Jazz Contest with the Natalia Calderón Quartet. In 2005 she formed her first group as a leader, a trio with bassist Carlos Barretto and drummer Andrés Litwin, releasing the debut album Lunas, Soles & Elefantes on the Basque label Errabal in 2008. A quartet featuring tenor and soprano saxophonist Ariel Bringuez, bassist Reinier Elizarde, and Litwin followed with La Espiral Amarilla (Errabal, 2011).

In 2011 Sánchez moved to New York City after receiving a Fulbright Scholarship to study jazz performance at New York University, where she earned a master's degree in jazz piano performance. She formed a new quintet built around specific bandmates: French-born tenor saxophonist Jérôme Sabbagh, Cuban-born alto saxophonist Román Filiú, Australian-born bassist Sam Anning, and California-born drummer Jason Burger. The group recorded her third album, Partenika, at Tedesco Studios in New Jersey in May 2014; Fresh Sound New Talent released it in April 2015, and The New York Times critic Ben Ratliff named it one of the ten best albums of the year.

The quintet's rhythm section changed for her next two records: bassist Rick Rosato and Israeli drummer Daniel Dor joined Filiú and Sabbagh on Danza Imposible, recorded at Brooklyn's Big Orange Sheep studio in March 2017 and released by Fresh Sound New Talent that December. NPR's Kevin Whitehead, reviewing it on Fresh Air, called the band a "Spanish-French-Cuban-Canadian-Israeli quintet" that "New York has a way of helping...get their time together," while All About Jazz praised Sánchez's ability to "discover wormholes" through conventional harmonic pathways. Chris Cheek replaced Sabbagh on tenor for El Rayo de Luz (2019), again with Filiú, Rosato, and Dor; DownBeat's Giovanni Russonello linked her hocketing melodic style and "chamber-jazz" writing to influences including Guillermo Klein, Carla Bley, Andrés Segovia, and Claude Debussy, and The New York Times named it one of the ten best jazz albums of 2019.

Sánchez was a composer in residence at the MacDowell Colony in both 2017 and 2021, where she began writing prepared-piano repertoire that would eventually become her first solo piano album. In 2022 she introduced yet another quintet lineup on SAAM (Spanish American Art Museum) (Whirlwind Recordings), with Filiú moving to tenor alongside new alto saxophonist Alex LoRe, bassist Rashaan Carter, and drummer Allan Mednard, plus guest appearances from trumpeter Ambrose Akinmusire and singer/guitarist Camila Meza on one track. She has also led a sextet with Meza, saxophonist/singer Charlotte Greve, vibraphonist/singer Patricia Franceschy, bassist Or Bareket, and drummer Jeremy Noller, and recorded a stripped-down trio session, Perpetual Void (Intakt, 2024), with bassist Christopher Tordini and drummer Savannah Harris. For the Space You Left, a full-length album of solo prepared piano drawing on the material she began at MacDowell, followed on Out Of Your Head Records in 2026.

Alongside her own dates, Sánchez has built a substantial career as a sideman and collaborator. Since 2022 she has been the pianist in saxophonist David Murray's quartet, performing with the group at the Village Vanguard in 2023 and 2024 and recording on Murray's albums Francesca (2024) and Birdly Serenade (2025), both for European labels. She has also recorded with vocalist/saxophonist Maria Grand, violinist Ludovica Burtone, saxophonist Alex Weiss, vocalist Indra Rios-Moore, clarinetist Oscar Noriega's Crooked Trio, and the Webber/Morris Big Band, and taught piano at NYU and in master classes across Central America. Her educational work has also included award-winning short-film scoring.

Sánchez writes intricate, polyphonic chamber-jazz compositions rooted in the Spanish folk tradition, often built around "hocketing," the old technique of passing a melodic line back and forth between voices, here typically her two saxophones. DownBeat's Giovanni Russonello traced her lyrical, unmannered writing to a mix of Guillermo Klein, Carla Bley, the classical guitarist Andrés Segovia, and Claude Debussy, while NPR's Kevin Whitehead singled out her use of "the Spanish tinge" (Jelly Roll Morton's phrase) and her taste for deceptively simple melodic cells inside otherwise demanding rhythmic frameworks. AllMusic classifies her work as avant-garde and post-bop jazz built for a small chamber ensemble rather than a conventional swinging rhythm section, and critics have consistently praised her for assembling international personnel, drawing players from Cuba, France, Israel, Canada, and Australia into cohesive working bands built around her own compositional voice rather than standard-repertoire blowing sessions.