The ex-France international was substituted at the interval of the clash in West London, having taken a knock in the first period in a challenge with Brentford's Ivan Toney.
After the match, Man United head coach Erik ten Hag said that Varane had been withdrawn «as a precaution».
Victor Lindelof was also substituted in the second period with what looked to be a hamstring issue, and the Sweden international will undergo a scan to determine the extent of the damage.
«I can't tell by now. Rapha we took him off as a precaution at half-time and Victor he came off but we have to assess him tomorrow,» Ten Hag told reporters when quizzed on the centre-back duo.
Varane will need to be assessed ahead of ChelseaVarane, while heading for the team bus, was asked about his injury, and the Manchester Evening News quoted him as responding «not too bad».
The 30-year-old has been an important player for Man United this season, making 29 appearances in all competitions, including 20 outings in the Premier League.
Varane spent a period earlier this season out of the team, but he has been a regular in recent months, with the Red Devils struggling with injuries in the middle of their defence.
Harry Maguire and Lisandro Martinez both featured off the bench at the Brentford Community Stadium, and the pair could be required to start against Chelsea in the team's next league match on April 4.
Varane will need to be assessed ahead of the contest at Stamford Bridge, but no risks will be taken with the experienced defender's fitness at this stage of the campaign.
Varane's future at Old Trafford Read on sportsmole.co.uk