Krenzel was named the Big Ten's player of the week after throwing for 273 yards and four touchdowns in OSU's pulsating 44-38 win over N.C. State.
But Tressel said Krenzel finished that game in pain after absorbing a second-quarter hit.
"He said it happened in the second quarter," Tressel said. "I know he had his adrenaline going and he was hurting, but I think he was like, `So what.'
"Then, on Sunday it was a little bit tighter. On Monday, it was still tight. The doctors made the decision he shouldn't be throwing today. It involves his elbow."
It is hoped that by resting Krenzel today he should be able to return to action in time for Saturday's game with Bowling Green.
"They have made a medical decision to rest him," Tressel said. "I don't worry about that. The score is that for today's practice the other guys will work. We have a great medical staff. It surprised me last week that they had Simon Fraser ready to go 84 plays."
Tressel said he takes a hands off approach to injury situations, even admitting he is unsure under new federal guidelines what he is allowed to discuss.
"About all I ask the medical people are, A, will you let him play? And, B, if he does play is there a chance of further injury? They tell us whether they can play or not. That way we can be realistic in our preparation up front. Then it's our job to decide how effective the player will be."
Tressel hedged when asked if Zwick or Smith would be considered the backup if Krenzel can't go.
"Right now, they would both play," he said. "As far as which one would play first, it would depend on what we're going to do on that particular set."