Morneau has not played since Wednesday night, when he suffered a mild concussion while taking an accidental knee to the head from Toronto's John McDonald on a slide into second base.
The 29-year-old has a history of concussions, including one he suffered in April 2005, when he went on the disabled list after being hit in the head by a pitch from Seattle's Ron Villone.
Morneau, who was voted in by fans as the starting first baseman for the AL, had said before Saturday's contest in Detroit that he would not travel to the All-Star Game if he did not play in Sunday's Tigers-Twins series finale.
"If I don't play here, I'm not going to go there," Morneau said. "Obviously, if I can't play for my team, I'm not going to fly out there and run around for two days."
The plan is for Morneau to be re-evaluated in Minnesota over the All-Star break. While the first baseman had shown some improvement by Saturday, Twins manager Ron Gardenhire said there is still no timetable for his return, as they'll see how Morneau is feeling when the team returns for the start of the second half on Thursday.
"It's one of those things where it's not completely gone yet, so we're not going to do it and then push it back or set it back a couple days," Morneau said of his headache on Saturday. "It feels like it's getting better. There is no reason to do anything today to make it worse."
This would have been the fourth consecutive All-Star Game for Morneau, who is batting .345 with 18 home runs and 56 RBIs and is near the top of the AL in nearly every offensive category. But it's the first time that he's been voted in by the fans as a starter.
Tigers first baseman Miguel Cabrera, who was first on the players' ballot for the All-Star Game, will get the start in place of Morneau.
"To play for somebody that is hurt, I don't like that," Cabrera said.
For the Twins, though, the biggest concern right now is not Morneau missing this critical series in Detroit or the All-Star Game, but just making sure that the first baseman gets back to feeling like himself.
"You are always concerned with a head injury," Gardenhire said. "He's getting better, but I can't foresee the future. I can't tell you what he's going to feel like in three days even. So we're just going to have to wait and see what he feels like after the All-Star break and go from there. If this thing is going to linger, he might end up on a DL stint. The bottom line is we're going to make sure he's healthy enough to play before we put him back out there."