Given impressed in his competitive debut for Villa, making a string of impressive saves to earn his new club a point.
Villa defender James Collins had to take the goal-kicks at Craven Cottage after Given indicated he had a problem.
McLeish will have to wait until the medics assess the problem before he knows the full extent of the injury.
"Shay had a bit of a tight groin," McLeish said. "That's why James Collins took the goal-kicks.
"But we're hoping he's okay. I need to speak to the doc. Twenty four hours is normally the time to tell."