Hudson's move is retroactive to July 24. He has a strain on his right side.
Morales batted .280 with one home run and 24 RBIs in 54 games with the Red Wings. He had surgery on his right wrist following last season after playing in 54 games with the Twins.
Minnesota announced the moves after Sunday's victory at Baltimore. The Twins were set to open a series Monday night at Kansas City.