The Millers captain has only just returned to training after breaking his collarbone in December.
Manager Ronnie Moore told BBC Radio Sheffield: "It's come up like a balloon so he's going to be 10 days to two weeks before he can get going again.
"He's chased after a ball and gone into a little divot that was on the pitch and done his ankle."
Cresswell broke his collarbone in the 1-0 win over Aldershot on 11 December.
Meanwhile striker Ryan Taylor is out of action for up to a fortnight with a groin injury he picked up in Saturday's defeat against Oxford.
Source: BBC Sport