The moves were made before Arizona faced the Cubs in Chicago on Friday.
Bloomquist has been on the disabled list all season with a strained right intercostal. He hit .467 in four rehab games for Triple-A Reno.
Chavez suffered a right oblique strain while swinging the bat at the plate early in the Diamondbacks' loss at Texas on Wednesday.
Chavez has been an important component in the Arizona lineup this season, hitting .325 with seven home runs and 25 RBIs, seeing more playing time than expected with the injuries to Bloomquist and second baseman Aaron Hill. Chavez has hit .394 since April 28 and had one error in 67 fielding opportunities.