Kolb was injured on the third play of Sunday's game against San Francisco. He was sacked and his helmet struck the knee of 49ers linebacker Ahmad Brooks.
He didn't play the rest of the game, as per NFL rules for a player with symptoms of concussion, which the Cardinals won 21-19 behind quarterback John Skelton. Kolb will be out an undetermined length of time, the team said.
"There are a number of different steps you have to go through and obviously player safety is very important," Whisenhunt said Monday. "I don't have a timetable on it."
It was Kolb's second start since missing four games with a foot injury.
Skelton, a second-year pro, completed 19-of-28 passes for 282 yards and three touchdowns in the Arizona win. On the season, he's 78-of-145 for 1,032 yards, seven touchdowns and nine interceptions.