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Rashford was replaced by Mason Greenwood in the 73rd minute after hurting himself while sprinting back to dispossess Riyad Mahrez on a dangerous City attack.
Ole Gunnar Solskjaer confirmed that Rashford had went over on his ankle but was unclear on the severity of the injury and said that the 23-year-old will undergo scans on the problem.
“I don't know. It's something with his ankle,” Solskjaer said.
“When he sprinted 70 yards to save a goal, it showed the attitude of the boy. I think he went over on his ankle but we need to do a scan, I've not had time to speak to the doctor yet."
Rashford is currently playing through the pain barrier with a persistent shoulder injury that he has carried since last season and may undergo surgery on the problem after this summer’s European Championships.
Solskjaer was delighted with United’s derby win, which was their third successive victory at the Etihad.
“You know, football, every game lives its own life, this season it's unpredictable, can go up and down, that's human nature,” he said.
“Today, I thought we started really brightly and on the front foot, when you get that 1-0 lead it sets a tone for the game, and I thought we were excellent the first 10 or 15.
“Then we settled into our shape, played too much on the result and we adjusted that at half time to be more positive again and the second goal was incredible. We're going to do everything we can to keep the performance level up every day.”