Cano was struck by a pitch from J.A. Happ in the first inning. Manager Joe Girardi said Cano was still dealing with pain and swelling.
Girardi said he hoped to have Cano in the lineup Friday night at home against Baltimore. Cano is batting .305 with 24 home runs and 85 RBIs.
The Yankees also were minus infielder Eduardo Nunez. He was scratched with a sore right knee.
Nunez fell after catching his cleat in a seam on the artificial turf Tuesday. He left an inning later and Girardi dubbed the tumble a "Nuney-ism."
The Yankees also had some fun at Nunez's expense Wednesday before he was scratched. There were laughs when teammates replaced the chair at Nunez's locker with a wheelchair, and used tape to make an imitation chalk outline near the spot where he'd fallen down behind second base.
A chuckling Nunez said he suspected Derek Jeter and Cano were behind the wheelchair prank, and pledged to make the culprits pay.
"For sure," he said. "I'm going to find out and do something to them."
Nunez acknowledged that he had developed a reputation for on-field incidents.
"Weird things happen to me all the time," he said.
Still sore, Nunez tested his knee during batting practice, but gathered his equipment and walked off the field with trainer Steve Donohue after about 20 minutes.
Jeter made his third consecutive start at shortstop after coming off the disabled list Monday for the third time this season, alongside Alex Rodriguez at third base.
Mark Reynolds was set to make his first major league start at second base. He finished up there Tuesday night after Cano and Nunez were hurt.
Before that ninth-inning stint, Reynolds had not played at second since 2007, his rookie season with Arizona.
Reynolds homered Tuesday night while another recent acquisition, Alfonso Soriano, hit two home runs.
Soriano has 11 homers and 33 RBIs since rejoining the Yankees in a July 26 trade with the Chicago Cubs. Girardi speculated that the 37-year-old felt more comfortable in New York's veteran clubhouse.
"The Cubs are a lot of kids," Girardi said. "It might be a little bit more difficult to relate, in a sense. Now he gets to be around people his age and it's probably easier."
Girardi also said right-hander Phil Hughes remains on track to make his next start Sunday. Hughes is winless in his last nine starts.
"We could address it," Girardi said of his rotation, "but right now that's what I have."