The Padres placed Morgan on the 15-day injured list Monday due to left knee inflammation.
The injury may have cropped up following Morgan's most recent relief appearance against the Dodgers on Friday, when he struck out two but allowed one run on two hits. He'll be replaced in the San Diego bullpen by right-hander Bradgley Rodriguez, who was called up from Double-A San Antonio. Morgan owns a 4.50 ERA, 1.77 WHIP and 26:13 K:BB across 22 innings in the majors this season.