The problem was first reported on Sunday by the New York Daily News, but has not been confirmed by team officials.
The newspaper said the veteran left-hander has a blood clot in the shoulder. If it is a clot, the injury likely will end his 2006 season, and could jeopardize his career.
"I'm hoping I'm back out there pitching this year as quickly as possible and hoping this is just an isolated incident," Glavine told the newspaper. "I'm also preparing in the back of my mind that it could be something worse than that. We'll find out."
Glavine, who has 287 career victories, is 12-6 this season with an ERA of 3.92 in 160 2/3 innings.
He is scheduled for a CT scan and an angiogram this week.