The Moroccan striker sat out Saturday's 1-0 Premier League defeat by Southampton after suffering the problem in the recent draw at Swansea.
Pulis had hoped Chamakh would make a swift recovery, but he will sit out this weekend's crucial clash against relegation rivals Sunderland and could also miss the trip to Newcastle and visit of Chelsea.
"We missed Cham's quality on Saturday. We're looking at two to three weeks out for him," he told the South London Press.
During his long spell at Stoke, Pulis put an emphasis on set-pieces, but the Eagles have rarely profited from dead-ball situations this season.
A record of just 19 goals in 28 Premier League games explains Palace's precarious position in the table and the manager has urged all his players to weigh in with goals.
"You can't just blame the forwards. What is a real disappointment is the lack of goals we have scored from set-plays," he said.
"The two centre-halves, Mile and KG - with people like that going into the box - we have got to get more goals off them. They are certainly big enough and there have been quality balls going into the box. The biggest thing in Premier League football is the top end of the pitch - it can be the difference at times.
"When was Damo's last goal? When did Mile score a goal from a set-play? They haven't so far but that doesn't mean they are not going to."