The Paducah Sun reported the 33-year-old father told police he had smoked marijuana at a Paducah restaurant where he works and then came home and had a couple of drinks.
McCracken County Sheriff Jon Hayden said the mother of the 5-week-old boy was awakened by his cries Monday morning and found him in the cold oven.
The baby was taken to a hospital where doctors found no injuries.
Long shares the home with the child's mother, 33-year-old Brandy S. Hatton.
The newspaper reported child welfare officials placed the infant and his siblings, ages 10 and 14, in the care of one of Hatton's relatives.
Long is charged with wanton endangerment.