The 29-year-old Gallo, a two-time All-Star and two-time Gold Glove winner, is batting .188 with a team-leading 11 homers and 23 RBIs in 46 games in his first season with the Twins. He also leads the team in OPS (.799).
Twins manager Rocco Baldelli said Gallo has been dealing with the injury for "a little while now."
He had been trying to play through the injury since suffering it May 14, but he had hit just .154 with 28 strikeouts in 52 at-bats since.
Gallo also missed 10 games in April while on the injured list with a right intercostal muscle strain.
In a corresponding roster move, the Twins recalled outfielder Kyle Garlick from Triple-A St. Paul. He has appeared in eight games for the Twins this season, batting .235 with two homers and four RBIs.
Baldelli is not with the team on Saturday as he deals with an illness. Bench coach Jayce Tingler served as acting manager in his place during the Twins' 4-2 loss to Cleveland.
Outfielder Byron Buxton and shortstop Carlos Correa were also out of the starting lineup for the second straight game. Buxton has sore ribs after being hit by a pitch on Thursday, and Correa is dealing with plantar fasciitis.
Reuters and The Associated Press contributed to this report.