Sanchez has been diagnosed with a right chest strain and has been placed on the DL retroactive to Saturday.
Soria suffered a left oblique strain.
Sanchez left the game Friday night in Toronto during the fifth inning after apparently tweaking something in his chest. He hits the DL for the second time this season after he missed more than half of May with a blister on his right hand.
Sanchez stats: 125 innings pitched, 8-5 record, 3.53 ERA, 102 strikeouts
The injury to Soria comes at an inopportune time for the Tigers. Soria was recently acquired to provide insurance to a bullpen that was struggling to finish games. On Saturday closer Joe Nathan spoiled an eight-inning gem by Max Scherzer and loaded the bases before being pulled by Brad Ausmus with just one out.
Soria came into the game and retired the first two hitters he faced to escape the jam and send the game into extra innings. When he came out to start the 10th inning he couldn't get through his warm-up pitches before exiting with the injury.
Soria stats:37.2 IP, 2-4, 3.58 ERA, 45 SO
Saturday's performance may have marked the end for Nathan as the closer, but Soria's injury will likely give the 39-year-old yet another chance to keep the job.
The Tigers will call up youngster Robbie Ray to fill Sanchez's spot in the rotation. Ray made three starts for the Tigers in May. In his first two outings he allowed just one run in 11.1 innings, but he was shelled for seven runs in his final start against Texas.
Ray stats: 15.1 IP, 1-1, 4.70 ERA, 9 SO
Kansas City has trimmed Detroit's lead in the AL Central to just 1 1/2 games heading into Sunday. The Tigers will have to rebound from these injuries quickly to stay ahead of the Royals, who are riding an MLB-best six-game winning streak.