Avila, in Sunday night's original starting lineup, had been playing with a sore right arm since he was hit between the elbow and wrist by a foul tip in the opener.
"The trainer told me just a little bit ago it's probably best not to go with him," Detroit manager Jim Leyland said. "In an emergency I'm sure he could go back there and catch the ball."
San Francisco led the series 3-0 heading into Sunday's game. Laird entered the night 0 for 3 in the series and Avila was 1 for 7.
Leyland wasn't sure what Avila's status would be if the Tigers won to extend the series.
"That would be a concern, to be honest with you," he said. "Alex is very tough, without question, one of the toughest I've ever managed. If it's hurting, it's hurting. But I would have to talk to our medical team about that."