Morneau's wife, Krista, delivered the couple's second child hours before Saturday's game against the Royals -- a boy weighing 7 pounds, 15 ounces and measuring 21 inches. Mourneau has a maximum of three days to be away from the team.
Manager Ron Gardenhire said Morneau will rejoin the Twins in Chicago for the White Sox series, but said he's not sure if Morneau will return Monday or Tuesday.
He's the second Twins player to be placed on the paternity list this season, as Josh Willingham also missed three days in late April to attend the birth of his third son.
Parmelee, meanwhile, hit .302 with four home runs and 18 RBIs in 28 games with Rochester. He entered Saturday's game against the Royals hitting .194 with two homers in 38 games with the Twins.
"Parmelee has been swinging well," Gardenhire said. "I talked to [Rochester manager] Gene Glynn today. He's hitting well against lefties and righties. So he's been playing really well. We have no issues with him coming up. He won't be overwhelmed and will be ready to go."