The 28-year-old France international picked up the injury in the first half of Manchester United’s 2-2 draw with Atalanta in the UEFA Champions League on Tuesday.
Varane only recently returned to action after missing three United games with a groin injury he picked up while on international duty with France.
Varane will miss this weekend’s Premier League game against Manchester City at Old Trafford as well as matches against Watford, Villarreal and Chelsea after the upcoming international break.
The former Lens defender will also have to sit out France’s upcoming FIFA World Cup qualifiers against Kazakhstan and Finland.
"The club confirms that Raphael sustained a hamstring injury, which is expected to keep him out of action for around a month," United said in a statement on Wednesday.
"We'd like to wish Raphael all the best as he works on his recovery."
Varane only joined Man United from Real Madrid at the start of this season and has taken in nine appearances across all competitions for Ole Gunnar Solskjaer’s side.
Varane’s absence will be a source of concern for Solskjaer, who is also sweating on the fitness of Victor Lindelof while Harry Maguire’s form has been unconvincing.
Man United will hope to have him back for the Premier League home game against Arsenal on December 2.
