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The France international was stricken after an awkward fall with an hour gone at Stamford Bridge and showed visible signs of concern, with less than a month to go before the World Cup in Qatar gets underway.
Varane covered his face while crying and was given support my his team-mates.
While he did not require a stretcher, showing displeasure at the offer and instead walking around the edge of the field with medical staff, the injury is a clear worry for both club and country.
Defending champion France has a number of injury concerns ahead of the defence of its crown, with Chelsea's N'Golo Kante to miss the tournament with a hamstring injury and Juventus midfielder Paul Pogba yet to return from a problem that has forced him to wait for his second debut with the Turin outfit.
France begins its FIFA World Cup campaign against Australia on 23 November, before taking on Denmark and Tunisia in Group D.