The moves were made Tuesday. Anderson has a sore left elbow and Ellis strained his right hamstring Monday night against Baltimore.
Anderson is 3-6 with a 4.00 ERA and was coming off successive poor starts against the New York Yankees and Boston Red Sox. He was 1-5 in his last eight starts.
Weeks, Oakland's first-round draft pick in 2008, was poised to make his big league debut as the leadoff hitter Tuesday night.
The A's also moved Dallas Braden from the 15-day DL to the 60-day DL.