The team announced the moves Wednesday before the start of the third game of a four-game series against the Indians.
Blevins joins the Athletics for the sixth time this season. He has a 3.80 ERA and no won-loss record in 19 outings.
Fuentes is 2-8 with a 3.96 ERA in 60 relief outings. The right-hander has 12 saves this year and has pitched well since July 4, compiling a 1.59 ERA over his past 22 appearances.
Fuentes is eligible to be reinstated Saturday when the Athletics host the Seattle Mariners in the second game of a three-game weekend set.