The 24-year-old French midfielder started against Basel as captain but limped off with a suspected hamstring problem in the first half and was reportedly seen leaving Old Trafford on crutches as his team eased to a 3-0 victory.
Manager Jose Mourinho told BT Sport following the game: "I don't know".
"It looks for me too (like a hamstring injury) but I haven't spoken yet to the medical department".
While Mourinho was still unsure about the extent of the France international's injury, the Portuguese tactician said Pogba could be missing for a few weeks.
"The squads are for these situations when we have injuries, we dont cry when we have injuries".
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I don't know who is the best at the moment but this is what I want - to be the best.
"No Paul for Sunday but we still have Herrera, Carrick, Matic and Fellaini".
United will face Everton next, in Sunday's Premier League fixture at Old Trafford, and Mourinho could give a further update on Pogba's condition when he conducts his pre-match press conference later this week. He pulled up sharp, he tried to carry on, he couldn't, and they took him off.
"I keep saying the same about Fellaini", Mourinho added.
"When you do that, if you do that, let's enjoy to play against the big guys".