Irwin was set to start Tuesday night's game against Houston in his Rangers debut. His only other major league appearance was a start for Pittsburgh on April 13, 2013.
Martinez has discomfort in his left side, and the move was retroactive to July 2.
Martinez is 1-6 with a 5.10 ERA over 16 games (11 starts) for the Rangers.
Irwin was 4-1 with a 2.41 ERA in seven games (six starts) for Round Rock. Texas got him on a waiver claim from Pittsburgh on May 28.