Conner suffered the injury during Sunday's practice. Conner has rushed for 108 yards on 27 carries during his six-year career.
Jones was released by Tennessee earlier in the week. He appeared in one game last season.
"Nothing serious at all," coach Rex Ryan said, per the Buffalo News. "He'll probably be a day, maybe two days max."
Miller was a third-round draft pick out of Georgia.
McKelvin is on the non-football injury list and has not been practicing as a result of the injury.