Morneau left to be with his wife Krista, who is expecting their second child. A player has a maximum of three days on the paternity list. Morneau is hitting .249 with 11 home runs and 40 RBI in 73 games.
The Twins recalled first baseman Chris Parmelee from Triple-A Rochester ahead of Saturday night's game against the Kansas City Royals. Parmelee hit .302 with four home runs and 18 RBI in 28 games with the Red Wings.
Earlier this season, he hit .194 with two homers in 38 games with the Twins.