Manager John Farrell says the exam Monday is partly to give Bailey "some peace of mind on what he's dealing with."
Asked Sunday if it was possible Bailey would have to go on the disabled list, Farrell said the Red Sox would "probably have more information on that" after the exam when the team gets back to Boston.
"We're not going to risk anything without a full checkup," Farrell said prior to Sunday's game against Texas.
Bailey last pitched April 28 against Houston, which was his fourth consecutive scoreless appearance. The right-hander has pitched in 13 games and converted five of six save opportunities.
Joel Hanrahan, who missed 15 games with a right hamstring strain, has four saves.
ESPNBoston.com's Randy Jennings and The Associated Press contributed to this report.