The 31-year-old was hitting .255 with 13 home runs and 43 RBIs in 38 games for Triple-A Salt Lake this season. He will join Minnesota's Triple-A affiliate, the Rochester Red Wings.
Carter, who led the National League with 41 home runs while with the Brewers in 2016, last played in the majors on July 4, 2017, for the New York Yankees. He hit .201 with eight homers in 62 games for New York.
The Twins lost first baseman Joe Mauer to the disabled list last weekend with a neck strain and concussion-like symptoms. Regular designated hitter Logan Morrison has started the past four games at first base.