Carrey, 51, had taken a dig at LaBeouf while presenting at the Golden Globe awards.
"Dying is easy, comedy is hard. I believe it was Shia LaBeouf who said that. So young, so wise," Carrey said while referring to LaBeouf's plagiarism of a graphic novelist and then his apology which in return was an uncredited quote from a rapper.
LaBeouf was quick to attack Carrey by questioning his parenting skills by tweeting: "The Jane Carrey Band. At least I don't get arrested for indecency on major LA highways! Or abandon love child's."
"Jim Carrey states that he is deeply involved in his daughter's life. I accept that, regret tweet on the matter. Apologies to both parents," Labeouf said.
He later seemed to praise Carrey in a new tweet: "If you explain Jim Carrey you've killed him, Nobody knows if it's for real or not. That way he's immortal."
LaBeouf has been the butt of jokes for plagiarising the work of graphic novelist Daniel Clowes and then for hiring sky-writer to paint "I am sorry Daniel Clowes" in the sky.