Morales will undergo surgery Sunday with ankle specialist Phil Kwong. The Angels did not release a timetable for his return, but the severity of the injury suggests it could be season-ending.
He was placed on the 15-day disabled list.
Morales has emerged as one of the game's up-and-coming stars. He finished fifth in MVP balloting last November and was leading the Angels in batting average (.290), home runs (11), RBIs (39) and total bases. He was the only Angel to play in all 51 games.
"This is bad," teammate Torii Hunter said.
The Angels players had surrounded home plate in anticipation of Morales' arrival. He flung his helmet aside and leaped as he reached the dish.
According to Angels manager Mike Scioscia, he did not land on a player's foot, but simply slipped on the plate and slipped, all 225 pounds landing on his turned ankle.
He collapsed and remained on top of home plate for several minutes, the Angels clustered around him. Trainers administered an air cast to Morales' left foot and he was placed on a stretcher and carted off the field.
Losing Morales for an extended period of time could be a crushing blow to the Angels' already-wobbly playoff hopes.
"It's a blow whenever you lose him for a couple days. Right now he's the best hitter on the ball club. He can really hit," Hunter said. "It really hurts the offense if he's out of the lineup."
Scioscia and general manager Tony Reagins both said the team will celebrate winning home runs in a different manner moving forward.
"It sure is exciting, but you always wondered if there's an accident waiting to happen," Scioscia said. "I know it's happened before."
Earlier in the game, Hunter left after being hit in the left hand by a Felix Hernandez fastball, but X-rays proved negative.
"I'm just worried about Kendry. He's one of our best hitters. To see a great moment go sour like that, it's pretty bad. Hopefully he's just got a sprained ankle or something small like that," Hunter said.
Mark Saxon covers the Angels for ESPNLosAngeles.com. Information from The Associated Press contributed to this report.