Barria was optioned to the alternate training site after Tuesday's doubleheader against the Astros.
The 24-year-old joined the active roster as the 29th man for the doubleheader, and he covered five frames in long relief during the matinee, allowing only one run. Barria has a 2.89 ERA, 0.86 WHIP and 8:3 K:BB through 9.1 innings this season.