Mench, who is batting .289 with five homers and 21 RBI in 41 games, suffered the injury in the first inning Sunday while throwing out Alex Rodriguez at the plate.
He was joined on the 15-day DL by oft-injured outfielder Brian Jordan, who started the season on the DL with a sprained MCL and is batting just .104 (5-for-49).
Matthews was having a solid year at Oklahoma, batting .324 with nine homers and 36 RBI. Allen, who played in just five games for the RiverHawks, was hitting .294 with no homers and two RBI.
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