Former England boss Roy Hodgson will replace him, BBC Sport understands.
The Eagles are 19th in the Premier League after losing 1-0 at Burnley on Sunday - and failed to score in their four league matches under De Boer.
Announcing the 47-year-old Dutchman's departure on the club website, Palace said: "We would like to thank Frank for his dedication and hard work."
Former Ajax boss De Boer only took over this summer, succeeding Sam Allardyce, who left after helping Palace avoid relegation last season.
His only win as Palace manager came in the EFL Cup against Ipswich Town.
Should Hodgson take the job on a permanent basis, he will be the club's seventh permanent manager in six years.
Palace chairman Steve Parish was at Turf Moor on Sunday, and said afterwards: "It's a terrible start but we have to stick together.
"People are frustrated, I'm frustrated, so are the management and players. We know we are better than this.
"I'm defending everyone at the club who is working their backside off to turn this around. Football teams lose games. It happens.
"Who has the better squad, us or Burnley? We had a much weaker squad when we finished 11th. The buck stops with me; I've never run away from that."
Speaking earlier this month, Parish had said De Boer's start had "not been great" and football was a "results-based business".
De Boer made two major signings at Palace, paying £26m for Liverpool centre-half Mamadou Sakho and signing Ajax defender Jairo Riedewald for £7.9m.
He also recruited full-back Timothy Fosu-Mensah and midfielder Ruben Loftus-Cheek on loan from Manchester United and Chelsea respectively.