The 20-year-old Dutchman injured his anterior cruciate ligament during the first half of a Capital One (League) Cup match at Swindon on Tuesday. Chelsea said in a statement that the surgery had been successful.
Van Ginkel, who joined the west Londoners in July from Vitesse Arnhem on a five-year contract, has made only two starts under manager Jose Mourinho.
He made his senior international debut last November and the layoff will be a blow to his hopes of selection for next year's World Cup in Brazil. Louis van Gaal's Dutch side have already qualified for the finals.