The child, whose parents are Busey and his fiancée Steffanie, remains hospitalised at LA's Cedars-Sinai Medical Centre while doctors monitor the undisclosed ailment, but Busey's spokesperson told TMZ that Luke is feeling better and will likely be able to return home later in the week.
"Gary is very grateful to his fans for their love and support," the star's rep said. "Steffanie and Gary thank everyone for their get well prayers for Luke."
Gary is also the father to daughter Alectra and son Jake, a fellow actor, who has starred in Starship Troopers and Enemy of the State.
Having been fired on the latest edition of Celebrity Apprentice, Busey has made a series of media appearances this week, including an interview on Jimmy Kimmel Live where he labeled his former teammates as "backstabbers".
The Celebrity Apprentice airs Sundays at 9pm ET/8pm ET on NBC.
> Meat Loaf: 'I'm friends with Gary Busey'