Erik ten Hag's side head to north London on Sunday for their final match before the international break without several key players.
Tyrell Malacia, Amad Diallo, Kobbie Mainoo and Tom Heaton have missed the start of the season and now experienced Varane faces a spell on the sidelines.
A club statement read: “Raphael Varane will be missing from the team when Manchester United face Arsenal in the Premier League on Sunday due to injury.
“The France international came off at half-time in our 3-2 win against Nottingham Forest at Old Trafford on Saturday due to the complaint, which is expected to keep him out for a few weeks.”
The PA news agency understands that United are expecting Varane to be back in less than the six weeks reported by some outlets.
The 30-year-old has dealt with a number of injuries since moving to Old Trafford in 2021 and, having retired from the France set-up in February, will have the international break to work towards his return.