Police spotted the alligator in a tank Friday when they were in the home on an unrelated matter.
It is the 20th alligator found on Long Island in the past year.
The Suffolk County SPCA and the New York state Department of Environmental Conservation responded and confiscated the animal.
It is illegal to own an alligator in New York state. The owners of the alligator found in Islip could be fined.
The Suffolk SPCA hosted a reptile amnesty program in September where people could turn their illegal pets in without facing charges.
SPCA Chief Roy Gross says the alligator found Friday was in good health. It will be sent to a safe location such as an animal sanctuary.