She was born in Egedesminde, Greenland, and was brought up partly in Greenland and partly in the Vesterbro area of Copenhagen. In 1991 she published her first book of poetry, Så længe jeg er ung (While I'm Still Young). Since 1993 she has been a full-time writer. In 1994 Naja Marie Aidt was awarded the Danish Fund for the Endowment of the Arts 3-year bursary.
Aidt is the winner of the Nordic Council's Literature Prize for 2008, for her short stories collection Bavian (The Baboon, 2006). The Bavian collection also earned her the Danish Kritikerprisen for 2006.