The Rays also currently have two starters (Yonny Chirinos and Charlie Morton) and backup Brendan McKay on the IL.
Chirinos, McKay, Kittredge and Poche all came out for the season.
Anderson leads the Rays in saves (three) and holds (four). He didn’t allow a deserved run in 11 appearances and had 15 strikeouts and a single walk in 9 1/3 innings pitched.
Despite the injuries, the Rays start Sunday’s games in first place in the American League East.
In other moves on Sunday, the Rays recalled left-hander Josh Fleming and right-hander Edgar Garcia at the major league club and nominated Sean Gilmartin for the assignment.
Fleming will start Sunday’s game against the Toronto Blue Jays.