Zavala went 1-for-4 with a solo home run in Sunday's win over the Athletics.
Zavala went 3-for-4 with an RBI single, a double and two runs during a win over the Rockies in Game 2 of a doubleheader Sunday.
The Mariners acquired Zavala from the Diamondbacks on Wednesday along with Carlos Vargas in exchange for Eugenio Suarez, Bob Nightengale of USA Today reports.
Zavala was claimed off waivers by the Diamondbacks on Wednesday, Daryl Van Schouwen of the Chicago Sun-Times reports.
Zavala (oblique) was activated from the 10-day injured list and designated for assignment Monday.
The White Sox announced Sunday that Zavala (oblique) will begin a rehab assignment at Triple-A Charlotte in the coming days, Daryl Van Schouwen of the Chicago Sun-Times reports.
Zavala was placed on the 10-day injured list Sunday with a strained left oblique.
Zavala is out of the lineup for Sunday's game against the Guardians, Daryl Van Schouwen of the Chicago Sun-Times reports.
Zavala will start at catcher and bat ninth in Wednesday's game against the Rangers.
Zavala is not in the starting lineup Friday versus the Twins.