Bedard, 5-2 with a 2.47 ERA in 11 starts, has not pitched since June 7. The 30-year-old missed a start in Colorado last weekend with the inflammation before being placed on the DL retroactive to June 8.
He is scheduled to see Los Angeles Angels orthopedist Dr. Lewis Yocum on Thursday. Yocum performed shoulder surgery on Bedard in September.
"I'm hoping this is just precautionary. We backdated the DL, which bought us some time," general manager Jack Zduriencik said before the Mariners played the San Diego Padres.
"What we're hoping for is that he's ready to go next week," Zduriencik said. "That's our best plans for him and we hope that happens. We'll know a little more after tomorrow. Nobody wants to take a chance. We're close, we're right here and Yocum's very familiar with him and what's gone on in the past."
Bedard, who can become a free agent after the season, didn't pitch last year after July 4. A cyst was removed from the shoulder during surgery in September.
The Mariners recalled first baseman Mike Carp from Triple-A Tacoma to replace Bedard on the roster.
Carp was brought up because Russell Branyan will miss Thursday's day game to attend his grandfather's funeral. Branyan is expected to be in Seattle in time for Friday night's game against Arizona.
Bedard signed a $7.75 million, one-year deal last winter to avoid arbitration and will lose money if he stays out long. He can make $600,000 in performance bonuses: $75,000 for 150 innings, $100,000 for 165 innings, $150,000 for 180 innings, $125,000 for 195 innings and $150,000 for 205 innings.