The 24-year-old limped off just 19 minutes into the game with a suspected hamstring injury and was later spotted leaving Old Trafford on crutches.
Speaking to MUTV last night, United boss Jose Mourinho said: "I don't know [how severe it is]. I just know from experience it's a muscular injury.
"In my experience, muscular injury stops you from playing for a few weeks, I think. It looks for me too [like a hamstring injury] but I haven't spoken yet to the medical department.
"Squads are for this, squads are for injuries, squads are for suspensions. We don't cry with injuries. So if no Paul for Sunday, we have [Ander] Herrera, we have [Michael] Carrick, we have [Marouane] Fellaini and we have [Nemanja] Matic."
Mourinho's men welcome Everton to Old Trafford in their next league game on Sunday afternoon.