Palace became the first side in Premier League history to lose their opening four fixtures without scoring a goal and De Boer paid the price, with his three-year deal terminated after a mere 77 days in charge.
The Dutchman was appointed by Palace on June 26, replacing former England boss Sam Allardyce after his surprise retirement.
Allardyce's predecessor as England manager, Roy Hodgson, is viewed as an early frontrunner for the Selhurst Park post.
The 70-year-old last managed in the Premier League with West Brom before leading the Three Lions at EURO 2012 and he has been tipped to sign a two-year deal at Palace.
Amid mounting speculation over De Boer's future on Sunday evening, Eagles chairman Steve Parish insisted everyone at the club must "stick together", although it seems he had a swift change of heart.
"Crystal Palace Football Club have this morning parted company with Frank de Boer," a club statement read.
"We would like to thank Frank for his dedication and hard work during his time at the Club.
"A new manager will be appointed in due course and we wish Frank the very best of luck for the future."
De Boer won four successive Eredivisie titles in his first head coaching role at Ajax, but now has two brief and high-profile failures on his CV after lasting 85 days at Serie A giants Inter Milan last season.
The 47-year-old's plans to move Palace away from the direct style they practiced under Allardyce flopped immediately as they suffered a comprehensive 3-0 defeat at home to newly-promoted Huddersfield Town on the opening day of the season.
A 1-0 loss at Liverpool followed before the gloom was slightly lifted with a 2-1 home victory over Ipswich Town in the EFL Cup second round.
But another home loss in the Premier League, Palace this time going down 2-0 to Swansea City, left de Boer on the brink heading into Sunday's trip to Burnley.
After Chris Wood's early opener set the Clarets on course to record a 1-0 win at Turf Moor, Scott Dann somehow missed a glorious late headed chance from close range. It proved to be the final straw.