The former Spain midfielder has been Barcelona boss since May 2014 and is in the final year of his contract.
Barcelona wrote on Twitter: “BREAKING NEWS: LUISENRIQUE21 announces he will not continue as Barça manager next season.”
Enrique has won eight trophies since taking charge, including the Champions League. He initially signed a two-year deal before agreeing a one-year extension at the end of a first season in which he won the treble.
The 46-year-old made the announcement after his side's 6-1 win over his first club Sporting Gijon on Wednesday night. Barça president Josep Maria Bartomeu had spoken of his wish to keep Enrique, but now he must look for a new boss.
The news will immediately ignite speculation over who will succeed Enrique at the Nou Camp. Sevilla's former Chile boss Jorge Sampaoli is among the early favourites for the role.
Everton's former Barcelona defender Ronald Koeman is another who has been linked with the job, while Tottenham manager Mauricio Pochettino has also been linked with Barça in the past.
There are likely to be no shortage of other candidates, with Arsene Wenger, the Arsenal manager, among them.
Wenger is out of contract at the end of the season and says he will still be in management even if he leaves the Gunners when his current contract expires at the end of this season after 20 years in charge.