Grigg has made 29 appearances for the Millers this term, scoring six goals, and his injury is a significant blow for Rotherham. The Northern Ireland international is not expected to be back until mid-March.
"Griggy coming off injured is a big blow. I think he is the glue to the team really," said manager Paul Warne.
"His link-up play is really good and he works well with Smudge [Michael Smith].
"Unfortunately, he's going to be out for a long period of time, so that isn't good news."
He continued: "I don't really like to put a timeframe on Griggy's because the physios told me, but we think he might be about eight weeks.
"His is a severe hammy. There was obviously nobody near him when he did it. He ran and put the cross in for a chance that Smudge should definitely have taken.
"It's a massive blow. Griggy has got back to looking really sharp and his offside goal was very harsh as well.
"He'll be out for a period. As I always say, it's 'next man up' but I do say that with a heavy heart because I do think we're going to miss him."
Defender Richard Wood will be available again after he was sent off in last weekend's 1-0 win over Accrington Stanley, having served his suspension against Wimbledon.
Warne added: "I think he has been one of our standout players, but he normally plays two in three, rather than every game.
"I try and protect the players wherever I can and we've managed the minutes quite well and kept the injuries down."
Mickel Millers is also out with a hamstring problem but Warne expects the forward to be sidelined for "another couple of weeks".