In exchange for the 34-year-old righty, the Dodgers will give the Twins either a player to be named later or cash considerations.
Correia is 5-13 with a 4.94 earned run average in 23 starts for Minnesota this season. He has 13 quality starts and 16 starts of six or more innings.
"Kevin gives us an additional option as a starter or long reliever," said Los Angeles general manager Ned Colletti. "He also supplies us with more veteran pitching depth for the stretch drive."
Over 12 seasons in the majors, he has played for San Francisco, San Diego, Pittsburgh and Minnesota. In 344 games (213 starts), he is 74-91 with a 4.53 ERA.