Love, who rushed for 2,118 yards last season and finished second in Heisman Trophy voting, left in the fourth quarter of Stanford's 17-3 win against USC with an apparent injury that was undisclosed.
The senior ran for 136 yards on 22 carries against the Trojans after being held to 29 yards on 18 carries the week before against San Diego State.
After the game against USC, Shaw told ESPN's Edward Aschoff that if Stanford had needed Love, he would have been able to finish the game.
"With the game in hand, we weren't going to put him back out there," Shaw said.
With Love unavailable, Cameron Scarlett is expected to start at running back for Stanford.