The Dutchman was drafted in to Craven Cottage over the summer as a replacement for the outgoing Mark Schwarzer, but sustained the problem on the opening day of the Premier League season.
That problem has since been aggravated in training, preventing the 31-year-old from returning to first team action.
With there no indication as to when the Holland international will be ready to return, an operation has become a distinct possibility.
Jol will give Stekelenburg until the international break to work on his fitness, but a decision will then be made on whether he needs to go under the knife.
"He will be out for the next two weeks and then we will make an assessment," Jol said. "He's got a few injections in his shoulder - it's quite sensitive and if it's not right in two weeks time he probably needs an operation.
"But the strange thing is that he trains with us. It's only a matter of over stretching all the time and then he feels a lot of pain. He had an operation on his other shoulder so we have to be very careful."
Jol had encouragement for England's David Stockdale who has come into the team in Stekelenburg.
He added: "I think Stockdale - and I told him as well - shouldn't consider himself as a number two," Jol explained. "But if there is another keeper ahead of you then you are a number two. But he was playing for Hull City [on loan last season] and he was the number one.
"I think he should behave as a number one; be vocal, be a personality in goal. Every time when he came in for Fulham - before I was here as well - he did very well. But a goalkeeper is always vulnerable."