The midfielder, in only his second start for Jose Mourinho's side since his switch from Vitesse Arnhem, tore his anterior cruciate ligament in Tuesday's League Cup win over Swindon.
The damage was confirmed by an MRI scan on Wednesday, his agent Rob Jansen told Dutch news agency ANP.
Jansen added the player would undergo surgery "in the next few days" and could be out for up to nine months.
His participation for Holland at the 2014 World Cup "is threatened", Jansen admitted.
Van Ginkel went down injured following an early challenge by Swindon's Alex Pritchard. Despite trying to play on, van Ginkel then went off in the 10th minute at League One Swindon's County Ground.
"We've got an injury to Marco which, it's a little bit too early to be certain but it doesn't look good," said Chelsea assistant first-team coach Steve Holland after the game.
Chelsea's Marco van Ginkel out for season, says agent
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