The move to the DL comes one day after Cueto said he needed time off because of his blister issues.
Cueto lasted only four innings in Friday night's start before being forced out by blisters on his right thumb and two other fingers on his right hand.
After the game, Cueto had bandages on the tips of his thumb, index finger and middle finger. He had problems with blisters on two fingers in May.
Cueto said the blister issues have made him feel "like a rookie" the way he's struggling. He won't throw again for five days.
"Of course I feel different now," Cueto said through a translator. "I think the best thing for me to do would be to take some time off. I'm not throwing very well and I don't want to hurt myself.''
Giants manager Bruce Bochy said Matt Cain will replace Cueto in the rotation. Bochy hopes Cueto will miss only two starts.
Cueto, who is 6-7 with a 4.59 ERA this season, said the blisters are caused by "the baseball -- the three fingers, I just can't feel the ball."
He said he thinks baseballs are wound tighter this year, and he noted that this is the first time he's had problems with blisters.
"I just can't explain it," he said. "I really don't know what's happening."
Blue Jays starter Aaron Sanchez has struggled with blisters this season and, like Cueto, has blamed a tighter baseball for his health issues.
Bumgarner, meanwhile, will start Saturday for the first time since spraining his left shoulder in a dirt bike accident three months ago.