Enyedi was born in Budapest in 1955. Her father, György Enyedi, was a geographer and economist who played a major role in the long-term development of regional science. She completed a B.A. in economics, studied film studies at the Academy of Drama and Film in Budapest starting in 1980, and also studied film in Montpellier. In the beginning, Enyedi created conceptual art and was a part of Balázs Béla Studio and the Indigo group.

Enyedi won the Golden Camera award for My 20th Century at the 1989 Cannes Film Festival. She began teaching at Academy of Drama and Film in Budapest (now known as the University of Theatre and Film Arts) that same year. In 1992, she was a member of the jury at the 42nd Berlin International Film Festival. Her 1994 film Magic Hunter was entered into the main competition at the 51st edition of the Venice Film Festival. In 2007, she was a member of the jury at the 29th Moscow International Film Festival. She received her doctorate from the University of Theatre and Film Arts in 2011.

Enyedi is married to author Wilhelm Droste, has two children, and lives in Budapest and Nordrhein Westfalen, Germany. In 2002 she was awarded with the Officer’s Cross of the Order of Merit.

In 2012 Enyedi was hired by HBO Europe to direct the Hungarian show Terápia, an adaptation of the Israeli show BeTipul about a therapist who spends his week helping others before getting his own psychological help. Enyedi described the project as “healing” after years of projects stuck in development hell. In total Enyedi directed 39 episodes over three seasons from 2012 to 2017.

Enyedi’s 2017 film On Body and Soul premiered at the 67th Berlin International Film Festival, where it won the Golden Bear. The film went on to be nominated for the Academy Award for Best Foreign Language Film, representing Hungary.

In 2018, she announced her next film would be an adaptation of The Story of My Wife, about a man who makes a bet with his friend to marry the next woman who walks into the café where they are eating. The film was adapted from a novel by Milán Füst of the same name.