The Rangers placed Urena on the 15-day injured list Sunday with right shoulder fatigue.
Urena (4-8) scooped up a win while working in long relief in Monday's 4-3 victory over the Pirates covering four scoreless innings and striking out three batters. He scattered two hits and two walks.
Urena (3-8) took the loss Tuesday as the Rangers were downed 9-4 by the Red Sox, coughing up six runs on seven hits and two walks over 4.2 innings. He struck out three.
Urena is scheduled to start Wednesday's game against the Astros at Globe Life Field.
Urena (1-5) took the loss Friday, giving up four runs (two earned) on four hits and two walks over 2.1 innings as the Rangers fell 8-2 to the Marlins. He struck out one.
Urena (lower leg) has been cleared to start Friday against the Marlins, Jeff Wilson of RangersToday.com reports.
Urena was removed from Friday's game because of swelling in his left lower leg, Kennedi Landry of MLB.com reports.
Urena will start Sunday's game against the Rockies at Coors Field.
Urena (1-2) earned the win Wednesday against Oakland, allowing two runs (one earned) on four hits and two walks over five innings. He struck out two.
Urena (0-1) picked up the loss to Houston on Saturday. He allowed five runs on six hits and one walk while striking out one over 1.1 innings.