Twins manager Ron Gardenhire said he opted to start Morneau at designated hitter in case he needed to leave Friday's game early.
"We're kind of on alert with that," Gardenhire said. "It's right at the due date now."
Once Morneau is placed on the paternity list, he has a maximum of three days to be away from the team.
Gardenhire said a player from Triple-A Rochester will be recalled to take Morneau's place on the roster once he is placed on the paternity list. First baseman Chris Parmelee is the most likely player to be recalled.