Sharps played in the 1-0 victory over AFC Wimbledon on Saturday, despite breaking his nose the week before, but, after picking up a fifth booking of the season, he will have to serve a one-game suspension at Meadow Lane.
The skipper's absence is likely to open the door for either Mark Bradley or Jack O'Connell in the heart of defence.
The former should be the preferred option providing he can prove his fitness following a groin injury.
Manager Steve Evans confirmed the rest of his side came through the Dons win unscathed and he will have further food for thought after Kieran Agard's match-winning cameo off the bench.
Both David Noble (ankle) and Dale Tonge (knee/ankle) have returned to full training, although Evans hinted their returns could come in a reverse-team clash against Stoke on Wednesday.
Should the Millers oust Keith Curle's side, Aldershot will be their third-round opponents.