Delon, who died Sunday aged 88, had said he wanted the Belgian malinois to be humanely killed and buried with him. But the foundation named after former film idol Bardot quoted Delon's family as saying the wish would not be carried out.
"Do not worry about Loubo," the foundation said in a post on the X social media platform.
"Many of you have sent us messages concerning the fate of Loubo," it added.
"'He has his home and his family', the family of Alain Delon have confirmed to us and they will take care of him. Loubo will of course not be euthanised."
Delon announced in 2018 that he wanted to be buried with the dog.
"He is my end of life dog. A Belgian shepherd who I love like a child," Delon told the Paris Match magazine.
"If I die before him I will ask the vet to let us go together. He will inject him so that he dies in my arms.
"I would rather that than knowing that he would let himself die on my grave with so much suffering."
Loubo was among the names given when the family announced Delon's death on Sunday.
"Alain Fabien, Anouchka, Anthony, as well as Loubo, are deeply saddened to announce the passing of their father," the actor's children said in a statement.
Two of Delon's sons posted on social media on Tuesday for the first time since the death. Anthony Delon posted three photos of his father in his younger days with the message "RIP Papa".
Delon's youngest son, Alain-Fabien, put up pictures of wreaths left outside Delon's home at Douchy in central France where he died.
