Stekelenburg had originally suffered the problem during the opening day victory over Sunderland, but the Dutch international has suffered a similar injury with his other shoulder.
The 57-year-old told Sky Sports News: "He fell on one shoulder and was out, and now he has fallen on the other one.
"He's in hospital now and we will take some pictures and monitor the situation.
"We will try again tomorrow to see if he can join us, but I don't think he will. Hopefully it's not serious."
The 30-year-old moved to Craven Cottage in the summer from Roma.