Melissa Aldana was born in Santiago, Chile. She began playing the saxophone when she was six, under the influence and tutelage of her father Marcos Aldana, also a professional saxophonist.
In 2013, aged 24, she was the first female musician and the first South American musician to win the Thelonious Monk International Jazz Saxophone Competition, in which her father had been a semi-finalist in 1991. The prize was a $25,000 scholarship, and a recording contract with Concord Jazz. Reporting her win, the Washington Post described Aldana as representing "a new sense of possibility and direction in jazz."