The Millers midfielder picked up the problem in Tuesday's 2-0 defeat by Watford after a challenge from Keith Andrews, which boss Steve Evans described as 'X-rated'.
Green, one of the early stand-out performers for the South Yorkshire club this season, had to be withdrawn and has undergone scans, making him a doubt for Saturday's trip to Millwall.
"It's an X-rated tackle, it's a red card, it's over the top, it's late," Evans said. "We don't know how bad it is, he'll have it scanned.
"He has been fantastic since he walked in through the door, he's a top professional and he'll want to get fit as soon as possible. It was a nasty one, though."
Meanwhile Evans confirmed sought-after striker Kieran Agard missed the game with a dead leg, but revealed he has been the subject of "aggressive" bids from an unnamed club.
The 24-year-old turned down a move to Leeds last week and will be given permission to talk to anyone who meets the asking price, thought to be around the £1million-mark.
"There was a football club bidding quite aggressively, whether they have reached the numbers the chairman wants I don't know," Evans added.
"Kieran couldn't have played because he had a dead leg picked up on Saturday.
"But if they reach the numbers then Kieran will get permission to talk and if he wants to go he can go, everyone has a price.
"Leeds have not come back in. I think Leeds made it quite clear publicly what they thought."