In the seventh inning, Bogaerts covered second when Willson Contreras attempted to steal it. Contreras' spikes appeared to slide into Bogaerts' left leg as Bogaerts tagged him out.
Chicago manager David Ross challenged the call, but it was confirmed upon review.
Bogaerts walked off the field after being assessed by the athletic training staff.
"He's doing OK," Boston manager Alex Cora told reporters after the team's 4-2, extra-innings win. "Seven [stitches] actually, right above the left knee. Right by the thigh. He's day-to-day. We'll see how it goes, how he feels during the flight and tomorrow."
Bogaerts said after the game that he felt OK, but wasn't sure if he'd be OK to play Monday's home matinee vs. Tampa Bay.
"I was lucky it wasn't my knee because that wouldn't have been good at all," he told reporters.
The 29-year-old is batting .318 with 31 RBIs this season. He went 0-of-3 with a walk before exiting.
Information from The Associated Press was used in this report.