Naylor was playing right field Sunday when he had a dangerous collision with second baseman Ernie Clement.
Naylor was carted off the field on a stretcher and showed visible distress, as did his teammates.
The team was playing against the Twins in Minnesota.
Cleveland reports Naylor suffered a closed fracture and dislocated his right ankle.
He received a full evaluation in Minnesota where he remained at the hospital overnight for pain management.
Naylor is scheduled to return to Cleveland Monday.
Cleveland Clinic foot and ankle specialist Dr. Mark Berkowitz will see him this week to determine the extent of the injury and a timetable for a possible operation.