The move is retroactive to Monday.
Crawford, 36, has dealt with soreness in the knee most of this season. It was hoped that time off around the All-Star break would help alleviate the issue.
But Crawford went 1-for-12 in a three-game set against the Pittsburgh Pirates coming out of the break and sat out the first two contests of the three-game series against the Cincinnati Reds that concludes Wednesday.
"He's been dealing with the soreness to some degree since spring training," manager Gabe Kapler said. "Some days, it's manageable. Some days, it's challenging. We thought it was a good time to give him a blow. We hope to get him back after the off day."
The three-time All-Star is batting just .207 with five homers and 24 RBIs in 64 games. Just two seasons ago, Crawford finished fourth in National League MVP balloting when he hit .298 with 24 homers and 90 RBIs in 138 games. He has spent all 13 seasons of his career with San Francisco.
The Giants recalled infielder David Villar from Triple-A Sacramento in a corresponding move. Villar, 26, batted .159 with five homers and 12 RBIs in 40 games with San Francisco earlier this season.
Rookie Casey Schmitt played shortstop the past two games and will draw his third straight start Wednesday night. The 24-year-old is batting .224 with two homers and 22 RBIs in 55 games.
Information from The Associated Press and Reuters was included in this report.