The Netherlands international lasted just 10 minutes of Tuesday's Capital One Cup tie following a challenge by Alex Pritchard, and will now sit out the majority of the season.
Van Ginkel, who only joined the club from Vitesse during the summer, was making just his second start for the club and is now not expected to return before April.
After the game, Chelsea assistant first-team coach Steve Holland said of the injury: "We've got an injury to Marco which, it's a little bit too early to be certain, but it doesn't look good.
"He'll have a scan on Wednesday on an injury to his knee. It's too early to say [if it's a bad one) but let's hope that's not the case.
"It didn't look good as he came off so early in the game. We'll have to see the results of the scan, we'll know more on Wednesday."
Fellow midfielder Ramires was another injury concern on Tuesday night, and is expected to miss Saturday's Premier League clash with rivals Tottenham.