The Athletics transferred Tarnok (hip) to the 60-day injured list Friday.
Tarnok's move to the 60-day IL will make him ineligible to return until May 28, though the A's were likely always going to take their time building him back up. The 25-year-old righty is scheduled to resume mound work soon and will likely require a minor-league rehab assignment before returning to Oakland's pitching staff. Brett Harris was selected from Triple-A Las Vegas to fill Tarnok's roster spot.