Rashford was taken off shortly after coming on as a substitute in their FA Cup win over Wolves .
He was thrown into the action in 64th minute, but had to be taken off again just over 15 minutes later after he went down clutching his back.
"It's a big blow because he's been by far and away Manchester United's best player, he's been their biggest goal threat," Scholes said.
"I think it's something that he actually picked up in the Manchester City game, where he got a bit of a knock on his back, but he played the Norwich game and was excellent on Saturday.
"This was an opportunity for him to have a break tonight and okay, it didn't work out because he had to come on as United were struggling a little bit but I think he'll be ok. Maybe a bit of ice and a couple of days rest but he'll be alright for Sunday."