The Red Sox said Bogaerts had a bruised right hand, and X-rays were negative. Bogaerts is day-to-day, according to manager John Farrell.
"Doesn't feel good," Bogaerts said of his hand. "We'll see how we come in tomorrow, but as of now it's very sore."
Asked if he was encouraged by the X-rays, Bogaerts said, "Yeah, I am, but I'm not encouraged by how it's feeling. But the X-rays tell a lot, so hopefully it feels better tomorrow when I wake up and put a lot of ice on it."
Bogaerts was batting with a runner on first base and one out when he was struck by a 1-2 pitch by Rays starter Jacob Faria.
Bogaerts was in obvious pain but stayed in the game to run the bases. He was replaced at shortstop in the bottom of the first by Tzu-Wei Lin, who moved over from third base.
Deven Marrero entered the game to play at third.