The former Vitesse player tore his anterior cruciate ligament during the Blues' 2-0 win over Swindon Town in the third round of the Capital One Cup on Tuesday evening.
Reports emerged after the game that the midfielder could miss the rest of the season, but Chelsea have suggested that he could return before the end of the campaign.
A statement on their official website said: "Chelsea Football Club can confirm Marco van Ginkel successfully underwent anterior cruciate ligament surgery today. The 20-year-old midfielder is expected to be out for approximately six months."
Meanwhile, the Blues are preparing to take on Tottenham Hotspur on Saturday.