Greene has a strained right shoulder, and Martin has a strained left hamstring. The Tigers reinstated left-handed reliever Daniel Stumpf from the disabled list and recalled outfielder Mikie Mahtook from Triple-A Toledo in corresponding moves.
Greene, who has 19 saves this season, pitched a scoreless ninth inning in Detroit's 9-1 victory over the Toronto Blue Jays on Sunday, but he had a noticeable decreased velocity on his fastballs, which were clocked between 91-93 mph. He told the team after the game that his shoulder had "been bothering him a little while," manager Ron Gardenhire told reporters.
"He came in a little frustrated," Gardenhire told reporters. "We've got to get this checked out. He can throw as hard as anybody, but it's not going anywhere."
Joe Jimenez will replace Greene, 29, in the closer role. He blew his first opportunity, walking in the tying run in the ninth inning Monday against the Blue Jays. He was credited with the victory, however, when the Tigers scored a run in the 10th and held on for a 3-2 victory.
The 23-year-old right-hander is 4-1 with two saves and a 2.93 ERA in 40 innings this season.
Martin, 30, also was on the DL in May because of his left hamstring. He is batting .257 with nine home runs and 29 RBIs this season.