The Chelsea manager said he was confident Palmer, who scored 15 Premier League goals last season, would not need surgery.
“We try to protect Cole as much as we can,” Maresca said. “The most important thing is when he comes back, he is fully fit.
“The medical staff are not magicians. We hope six weeks are enough. We need to see it step-by-step. For sure, he’s going to be OK.
“He looks relaxed. He has tried to recover from the injury and is doing all the therapy.”
Speaking before his side continue their Premier League campaign away at Nottingham Forest on Saturday, Maresca conceded Palmer would be a big miss.
“To replace Cole is difficult, because Cole is a very important player for us – probably one of the best players in the Premier League – so to replace that kind of player is always difficult,” he said.
“We don’t have another player like Cole, because Cole is unique.”
Palmer will miss Premier League games against Sunderland, Chelsea, Tottenham Hotspur, Burnley and Arsenal, and a League Cup tie at Wolves.
The six-week recovery estimate would also count Palmer out of Champions League games against Ajax, Qarabag and Barcelona, while ruling him out for England’s upcoming World Cup qualifiers against Serbia and Albania.