The Dutch defender will wear a protective mask in the fourth-round tie at Meadow Lane after picking up the injury in the victory against Wolves at the weekend.
Manager Roberto Martinez praised Melchiot's attitude.
"Mario is setting the right example as skipper of the club," said the Latics boss. "It will take a lot more than that to keep him away from the pitch.
"It is a straight fracture, it hasn't stopped him training, and he will play with a mask. He should fine, which is great news."
Paul Scharner could also be fit to face the League Two side after suffering a swollen ankle and knee against Wolves.
"We will assess him over the next couple of days," added Martinez.