Manager Alex Cora said the three-time All-Star was "pretty sore."
"He texted me early. He was my wake-up text," Cora said. "It was a big cut. Hopefully, he feels better tomorrow, and we can use him."
Bogaerts was injured in the seventh inning of Sunday's 4-2 victory at the Chicago Cubs when he covered second and Willson Contreras' spikes slid into the shortstop's left leg as Bogaerts tagged him out.
Bogaerts is hitting .318. The Red Sox opened a three-game series against the Rays before hosting the AL East-leading Yankees for a four-game series that starts Thursday.
The Associated Press contributed to this report.