Martin was placed on the 15-day injured list Tuesday with a left shoulder strain.
Martin was previously listed on the bereavement list, but the move to the 15-day IL will end his season as the Rangers have just 10 games left this year. The 27-year-old lefty will finish the season with a 1-7 record and three saves to go along with a 4.14 ERA and 1.36 WHIP.