He has been replaced by former Eintracht Frankfurt coach Oliver Glasner. The 49-year-old German signed a contract to the end of the 2025/2026 season.
The Monday afternoon (Tuesday AEDT) changing of the guard came hours before Palace were due to play a Premier League match away to Everton.
Hodgson's right-hand man Ray Lewington was due to lead the team at Goodison Park, with the Eagles just five points clear of their opponents who are in the relegation zone.
Former Frankfurt coach Oliver Glasner has signed to Crystal Palace to the end of the 2025/26 season. (EPA PHOTO)
A Palace statement said former England manager Hodgson was "out of hospital and doing well".
The Eagles have lost 10 of their past 16 league games and it was widely reported that Hodgson was on the brink of being sacked when taken ill last week.
"I understand, given recent circumstances, it may be prudent at this time for the club to plan ahead," Hodgson said in a statement by Palace, "and therefore I have taken the decision to step aside so that the club can bring forward their plans for a new manager, as intended for this summer."
Hodgson was in his second spell in charge of Palace, having returned in March last year having been manager from September 2017 to May 2021. He previously managed many clubs and national teams across Europe and beyond in a 48-year coaching career including Liverpool, Switzerland, Inter Milan, Finland and Fulham.
Glasner coached Eintracht Frankfurt for two seasons, leading the Bundesliga club to Europa League triumph in 2022 and the German Cup final in 2023. He was previously at Wolfsburg.
"I'm delighted to welcome Oliver to the club. He has an outstanding record, and we believe he is the right manager to take the club forward at this pivotal stage," chairman Steve Parish said.
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