Morneau will miss the game Tuesday night in Anaheim, Calif., because of a concussion. The Twins' slugging first baseman withdrew Saturday, following a doctor's advice, and will return to Minnesota to rest during the break.
New York Yankees manager Joe Girardi, the American League skipper, selected Konerko to be Morneau's replacement on the roster. The Chicago White Sox first baseman began the day batting .299 with 20 home runs and 62 RBIs.
Morneau didn't play Saturday, missing his third straight game, and won't be in the lineup for the series finale against the Detroit Tigers on Sunday.
"If I can't play for my team, I'm not going to be playing for the American League," he said before the game.
Morneau was evaluated Saturday by Dr. Kenneth Podell, a concussions specialist who consults with pro teams in Detroit.
Tigers bopper Miguel Cabrera will take Morneau's starting spot at first base for the AL because he was picked by players to be on the team.
Morneau was accidentally kneed in the head by Toronto's John McDonald on Wednesday. Morneau slid into McDonald while trying to break up a double play at second base. He walked off the field without assistance but didn't return.
"I feel better, but the headache is still there," Morneau said. "There's no sense trying to do anything and set myself back two or three days."
The four-time All-Star is hitting .345 with 18 home runs, 56 RBIs and 25 doubles. He ranks among the league leaders in all those categories and was elected by fans to start Tuesday night at Angel Stadium.
Morneau went on the disabled list four years ago after he was hit in the head by a pitch from Seattle's Ron Villone and had headaches for several days, leading to him missing 13 games. The Canadian also had head injuries during his days as a youth hockey goalie and high school basketball player.
"You're always concerned about a head injury," Minnesota manager Ron Gardenhire said. "He's getting better, but the bottom line is that we're going to make sure he's healthy before we put him back on the field. There's no timetable."