Erik ten Hag's side head to north London on Sunday for their final match before the international break without several key players.
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.