Manager Buck Showalter said Lindstrom is scheduled to have an MRI after an examination with Dr. John Wilckins on Friday revealed a significant injury.
"After examining him, [he] said it would be a while, at least the DL period," Showalter said. "Until we get the reports back, I'm not going to project it."
Lindstrom has a 1.29 ERA and has struck out 14 in 13 games. He gave up three runs, two of which were earned, in Thursday's loss to the Rangers, in the nightcap of a doubleheader -- the first time he's given up an earned run this season.
Although Lindstrom was examined by team trainers in the dugout after his outing, he downplayed the significance of the injury following the game.
"I kind of felt a pop on it on one of my two-seam fastballs," Lindstrom said Thursday. "But it's nothing serious at all, just a little soreness in my middle finger. It's fine."
Lindstrom has struggled with injuries throughout the 2012 season, dealing with back and hamstring issues as early as Spring Training.
The Orioles also designated infielder Zelous Wheeler for assignment to open a space for Eveland on the 40-man roster.