McCarthy said Jennings and offensive tackle Marshall Newhouse, who also suffered a concussion in the scrimmage, would be evaluated later in the week.
"I wouldn't rule Marshall or Greg out this week," McCarthy said, according to the Green Bay Press-Gazette. "I know they're going through the protocol. I'll probably know more Tuesday."
Jennings had 67 catches for 949 yards and nine touchdowns last season in 13 starts.