Belt, who was placed on the DL, will have two pins surgically installed in his thumb on Tuesday. They will be removed after four weeks, and Belt would then go through two weeks of rehab.
Belt, who led the club with nine home runs entering Saturday, broke his left thumb Friday night when he was hit with a pitch by Dodgers pitcher Paul Maholm.
"When they take the pins out, you'll have a better idea of where you're at, how much baseball activity you can do and how much you can ramp up your rehab," Bochy told the San Francisco Chronicle on Sunday. "He'll definitely have to play some games in the minor leagues."
Bochy has said that left fielder Michael Morse will get the bulk of the playing time at first because of his experience there.
The Associated Press contributed to this report.