The move is retroactive to Monday.
Thairo Estrada was recalled from Triple-A Sacramento.
Belt exited a 6-2 win at Colorado on Sunday in the seventh inning after getting hit on the left hand with a pitch while squaring to bunt.
On Monday, the Giants said an X-ray showed the broken bone and that Belt will "continue to meet with doctors over the next couple of days to develop a recovery plan and timetable for his return."
The injury is a big blow for the NL West leaders, who began a home series with the Diamondbacks on Tuesday night still seeking to close out their first division title since 2012.
The 33-year-old Belt is batting .274 with a career-high 29 homers and 59 RBIs.
Information from The Associated Press was used in this report.