The midfielder was replaced after 19 minutes by Marouane Fellaini during United's 3-0 win over Basel in the group stage.
With club captain Michael Carrick on the bench and Antonio Valencia, who has taken the armband in every game this season, rested completely, Jose Mourinho had given Pogba the captaincy for the first time.
However, Pogba failed to last 20 minutes of the Group A encounter at Old Trafford after stretching awkwardly to win the ball in midfield.
The France international immediately held his hamstring and signalled to the bench for assistance after only being able to take a few steps.
The 24-year-old limped off the pitch as Mourinho turned to Fellaini, who missed the weekend's 2-2 draw at Stoke City, to fill the void in midfield.
And he was forced to leave the stadium on crutches as United await medical reports that will determine the severity of the injury.
Pogba has been in superb form for United this term, netting twice in the opening fives games and any prolonged absence would represent a significant blow as a packed fixture list awaits now that European football has returned.
United, who are unbeaten after four Premier League fixtures, host Everton at Old Trafford on Sunday.
Pogba had initially been chosen to lead a line-up featuring two enforced alterations, with Victor Lindelof handed a second start for the club alongside Chris Smalling due to Eric Bailly and Phil Jones being suspended.
Ashley Young was picked for the first time this term at right-back, while Juan Mata and Anthony Martial returned to the XI in place of Ander Herrera and Marcus Rashford respectively.
United, playing in the Champions League for the first time in two years, entered the contest on the back of an unbeaten start in the Premier League.