The Athletics optioned Alvarez to Triple-A Las Vegas on Wednesday.
Alvarez is out of the lineup for Sunday's game against the Orioles.
Alvarez went 1-for-3 with a walk, a stolen base and two runs in a loss to the Angels on Wednesday.
Alvarez went 3-for-4 with a double, an RBI single and a run during Tuesday's 7-5 loss to the Angels.
The Athletics selected the contract of Alvarez from Triple-A Las Vegas on Saturday.
The Athletics reassigned Alvarez to minor-league camp Sunday.
Oakland signed Alvarez to a minor-league contract Wednesday with an invitation to major-league spring training.