Van Ginkel, 20, suffered a serious injury in the first half of Chelsea's 2-0 League Cup win over Swindon Town on Tuesday.
And the club revealed on Thursday that the Netherlands international has now had an operation on his anterior cruciate ligament.
Van Ginkel will face a race against time to feature in the final stages of the season, and is also now a doubt for his country's FIFA World Cup campaign.
The playmaker only signed for Chelsea in June, joining from Vitesse after starring for the Dutch club that Chelsea have a partnership with.
The highly rated prospect scored 12 goals in 45 appearances in all competitions last season for Vitesse, who currently have six players on loan from Chelsea.
Van Ginkel has made four appearances for Chelsea this season.
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