The side-arming right-hander was bothered by soreness in the middle finger of his throwing hand, but he threw a bullpen session before Thursday's game against Cleveland and felt good.
Manager Ron Gardenhire said Neshek would only be available in an emergency because of the pre-game throwing session, but he'll be at full strength for the weekend series at Kansas City. Neshek last pitched more than a week ago, throwing two scoreless innings on April 14 against Boston.
Mijares is better, but will stay in Minnesota to rehab during the next road trip. Condrey felt discomfort in his last bullpen session, though, and is not close to returning.