The 40-year-old right-hander recorded a one-out save on Opening Day, striking out former teammate Torii Hunter on a controversial check swing call.
Nathan is the second relief pitcher the Tigers have placed on the disabled list this season, after Bruce Rondon was shelved with tendinitis in his shoulder. Joakim Soria is expected to close for Detroit in Nathan's absence.
Nathan had his worst season as a reliever in 2014. He blew seven save attempts, tied for second most in the American League, and posted a 4.81 ERA that was worst in baseball among anyone with 20 or more saves.
Since missing the 2010 season after undergoing Tommy John surgery, Nathan has averaged 61 appearances a year.
A six-time All-Star, Nathan is currently the active saves leader with 377 career saves, seventh all-time.
- Alex Putterman