Walton isn't in the Giants' lineup for Tuesday's game against Arizona, Maria I. Guardado of MLB.com reports.
Walton is not in the lineup for Monday's contest versus the Diamondbacks.
Walton is out of the lineup for Sunday's game against the Royals.
Walton will start at second base and bat ninth in Thursday's game against the Orioles, Shayna Rubin of the San Francisco Chronicle reports.
The Giants selected Walton's contract from Triple-A Sacramento on Friday.
Walton signed a minor-league contract with the Giants on Dec. 23.
Walton (shoulder) was reinstated from Triple-A Sacramento's 7-day injured list Friday and assigned to Double-A Richmond. He's gone 2-for-9 with two strikeouts in his first two games with Richmond.
Walton (shoulder) is hitting .250/.340/.318 with four walks against 11 strikeouts in 12 games since moving his rehab assignment to High-A Eugene on June 25.
Walton (shoulder) began a rehab assignment Friday with the Giants' rookie-level Arizona Complex League affiliate and has gone 3-for-6 with a double, a walk and two runs in two games.
Walton underwent shoulder surgery during the offseason and isn't expected to return until May, Susan Slusser of the San Francisco Chronicle reports.