Montero had his contract selected from Triple-A Nashville on Monday.
Montero will replace the injured Shawn Kelley (biceps) on the roster and in the bullpen. The 28-year-old underwent Tommy John surgery last year and hasn't pitched in the majors since 2017 as a result, though he owns a solid 3.44 ERA, 1.04 WHIP and 31:2 K:BB across 18.1 minor-league innings this season.