The 3m missile was found by police investigating a 51-year-old man living in the North East suburbs of the city.
A man has been charged with possessing dangerous article,s unlawful possession of unregistered and insecure firearms.
The heat seeking Sidewinder missile is primarily used in air-to-air combat between fighter jets, but may be deployed to attack ground targets.
The missile discovered in Adelaide was expended and disarmed when police found it.
An investigation has been launched as to how the missile came to be in Adelaide.