Van Ginkel, a £8.4m summer signing from Vitesse Arnhem, suffered the knee injury during the Capital One Cup win over Swindon Town.
The Dutchman - making only his second Chelsea start following his summer move - went down after a challenge from Alex Pritchard and hobbled off the pitch in the 10th minute.
A club statement said: "Chelsea Football Club can confirm Marco van Ginkel successfully underwent anterior cruciate ligament surgery today (Thursday).
"The 20-year-old midfielder is expected to be out for approximately six months."
Van Ginkel had moved to west London in the summer on a five-year contract from Arnhem after coming through the Eredivisie club's youth system.
The Holland international will hope to return to fitness in time to put himself in contention to make his nation's World Cup squad for Brazil next year, after making his full international debut last November.