The France international had to be replaced during the early stages of the second half of United's Europa League last-16 second leg against FC Rostov with Marouane Fellaini coming on in his place.
The Red Devils were still able to win the game 1-0, Juan Mata scoring the only goal as they advanced to the last eight of the competition 2-1 on aggregate.
However, Mourinho has been left counting the costs of the win after watching Pogba limp off, while the Portuguese also has concerns over Marcos Rojo, who struggled to finish the game.
Asked if he thought Pogba would be out for three weeks, Mourinho replied: "Yeah.
"I don't know for sure but, for sure, no Middlesbrough [on Sunday] and no national team."