Rice sustained a hip flexor strain in Sunday's 14-6 win over the Cleveland Browns and left in the fourth quarter. He didn't have an MRI and didn't appear to be limping after the game.
Rice has played in 66 straight games, the third-longest current streak on the Ravens.
"That's the indication, that it's not really serious," Harbaugh said. "They would be looking at it if they thought it was. So, we'll just be day to day with him. I'd probably lean toward resting him this week and see how he looks this weekend. He's not going to need the practice to play in the game. If he feels great, we'll put him out there. If he doesn't, we'll probably rest him and get him ready to go Sunday if possible."
If Rice can't play, he would be replaced by Bernard Pierce, who leads the Ravens in rushing with 79 yards.
"He's becoming a complete back," Harbaugh said. "We're just very fortunate to have him on our team."
After Sunday's game, Browns defensive tackle Phil Taylor insinuated that Rice spat on him, which led to Taylor slapping the side of Rice's helmet.
Harbaugh hasn't spoken to Rice about the altercation with Taylor, but the coach was made aware of the situation.
"I watched it, and I didn't see that on tape at all," Harbaugh said.
Meanwhile, the Ravens gave permission to QB Joe Flacco to skip Monday's practice and remain in New Jersey, where his wife gave birth to their second son on Sunday. Harbaugh has remained in communication with Flacco through texts.
"He seems pretty happy," Harbaugh said.