The League One rivals go into the weekend's contest on the back of 1-0 wins on Tuesday night, with the Owls claiming an impressive victory over second-placed Wigan Athletic at Hillsborough while the Millers won at AFC Wimbledon.
His replacement Joshua Kayode made an instant impact as he scored the only goal of the game four minutes after coming on.
"I think it is his hammy, it looked like his hammy the way he was down and holding it," said Warne of Grigg's injury.
"As soon as he went down, we knew there was a problem. The early signs aren't great."
Rotherham are also expecting to be without Mickel Miller for at least a month after the forward picked up hamstring problem.
He was a second-half substitute as the Millers beat Accrington Stanley 1-0 on Saturday but he was not part of the squad at Wimbledon on Tuesday night.
Warne added: "Mikel has got a hamstring issue, I don't see him playing for at least a month which is a big blow.
"It seems in the last seven days we have had a few issues. It is always going to happen, we have probably rode our luck a little bit. We have got a few wounded bodies but we have enough to put a team out."
Ollie Rathbone was absent on Tuesday with a back problem but Warne is hopeful he will be available against Wednesday.