Detroit sent minor league left-handed pitcher Cole Nelson and a player to be named later in return for Young, who has struggled this season after helping Minnesota win the division crown last year.
The Tigers, who are opening a series against Minnesota on Monday, are missing outfielder Brennan Boesch to a sprained thumb, have Carlos Guillen on the disabled list with a sore wrist and have had designated hitter Victor Martinez hobbled by a sprained knee.
The 25-year-old Young was batting .286 with just four home runs and 32 runs batted this season.
Last year Young, who is eligible for arbitration this winter and could file for free agency after next season, batted .298 with 21 home runs and 112 RBIs.
Nelson, a 10th-round selection by Detroit in last year's draft, went 5-11 with a 4.87 ERA for Class A Lakeland. He struck out 87 batters in 105 1/3 innings, but also walked 50.
It was the first trade between the division foes in 10 years.
The 64-56 Tigers were leading the AL Central by 2.5 games over the Cleveland Indians. Minnesota (52-67) trailed Detroit by 11.5 games in the standings.
(Reporting by Larry Fine in New York, Editing by Rex Gowar)