Gaither was injured in last Saturday's accident at the Cowboys' indoor practice facility.
Cowboys scouting assistant Rich Behm and special teams coordinator Joe DeCamillis remain hospitalized following surgery. Behm had surgery to stabilize a fracture to the Thoracic spine (10th Thoracic vertebrae), an injury that caused paralysis from the waist down. DeCamillis had surgery Monday to stabilize fractured vertebra in his neck and should be released from the hospital later this week.