The 23-year-old England international has been out since coming off in the first half of Chelsea's 2-1 defeat at Manchester United on 20 September.
Maresca had initially hoped Palmer would return following the October international break, but the Italian admitted on Friday that the midfielder's recovery would take longer than expected.
"I was wrong. Unfortunately, he needs to be out probably six more weeks," Maresca said. "This is the update. We are trying to protect Cole as much as we can, and the most important thing is that when he comes back, he's fully recovered."
Maresca also confirmed that Palmer will not require surgery, describing the situation as "frustrating but manageable". The playmaker's absence leaves Chelsea short of attacking options, with Enzo Fernandez also sidelined.
The manager admitted that finding a replacement for Palmer's creativity and goal threat will not be easy. "For sure, we need to find a different solution, different skills, because we don't have another player like Cole," Maresca said. "Cole is unique. He's one of the best players in the Premier League."
Palmer has been one of Chelsea's standout performers since joining from Manchester City in a deal worth around £40 million in 2023, scoring 16 league goals in his debut season.
Chelsea, who are aiming to climb back into the top six from their current seventh-place position, face Nottingham Forest at the City Ground on Saturday, with Maresca urging his players to "step up and adapt" during Palmer's absence.
Liverpool's dominant 5-1 Champions League victory over Eintracht Frankfurt was overshadowed by a major injury setback, as Jeremie Frimpong suffered a recurrence of his hamstring problem that will keep him out for several weeks.
Manchester City are facing several late fitness tests as they prepare to visit Aston Villa on Sunday, with key midfielder Rodri among those in doubt.
Arne Slot said Liverpool's dominant 5-1 Champions League victory at Eintracht Frankfurt had been the perfect response to their recent struggles, describing it as "a big, big difference" from their previous performances.
Chelsea manager Enzo Maresca has said he was "very proud" of his young players after the Blues demolished Ajax 5-1 in the Champions League at Stamford Bridge on Wednesday night.
