The Sweden international went down off the ball holding his leg and went straight down the tunnel after being replaced by Phil Jones at the heart of the United defence with the scores tied at 0-0.
Lindelof is arguably United's most consistent performer in central defence and Ole Gunnar Solskjaer hopes the injury is not too serious.
He is still waiting on updates from his medical staff.
Tahith Chong was another to take a knock for United as they edged out Inter courtesy of a solitary strike from Mason Greenwood.
The Dutch youngster is not expected to be forced onto the sidelines, but the diagnosis for Lindelof remains unclear.
Solskjaer told MUTV when asked for a fitness update: “We don’t know yet but [Lindelof and Chong] should be OK.
“Victor, we’ll have to assess him tomorrow but Tahith will be fine. It’s just a knock. I don’t blame the defenders for trying to stop him.”
While injury setbacks could cast a cloud over United’s outing against Inter, there were plenty of positives for them to take from the game.
Talented teenager Greenwood caught the eye once again as the match winner.
The Red Devils also kept a clean sheet against a team now working under the guidance of former Chelsea coach Antonio Conte.
Results at this stage count for little, with pre-season all about working on sharpness and trying to iron out any faults.
Solskjaer believes his side are doing just that, adding: “I think we got what we asked for.
“The conditions were tough but I thought it was excellent with some pressing.
“In the first half, I thought we pressed really well and won the ball it was just that final little bit was missing. Of course, in the second half, we got a goal.”
United’s next outing, which could come with or without Lindelof at their disposal, will see them face Premier League rivals Tottenham in the International Champions Cup on Thursday.