Pogba was not included in Ole Gunnar Solskjaer's matchday squad having picked up the problem during France's 4-2 Nations League win over Sweden earlier this week.
The 27-year-old was unable to complete at training session at United's Carrington base on Friday and faces a race to be fit for Tuesday's Champions League tie against Istanbul Basaksehir.
"Paul's got a knock in the last game," Solskjaer told MUTV before kick-off against West Bromwich.
"He started feeling it yesterday before the session and he couldn't carry on. Hopefully he'll be OK for Tuesday but we don't know."
Solskjaer made two changes to the side which beat Everton at Goodison Park before the international break, with Alex Telles handed a Premier League debut at left-back.
Telles replaced the injured Luke Shaw while Nemanja Matic came in for Scott McTominay in midfield. Mason Greenwood, who is struggling with an illness, was absent from the squad.