Officials have not said how the person was killed. The BBC has contacted local police and fire authorities, as well as park officials.
Witnesses told local media they saw a man ejected from the ride, accounts that the BBC has not verified.
Local outlet 11Alive quoted, external a witness saying the man fell from the rollercoaster on to the roof of a haunted house attraction.
A park spokesperson said in a statement that its team and local authorities had responded immediately, and they were co-operating on an investigation into the incident.
Mableton Mayor Michael Owens said the city's public safety director was co-ordinating with local police and park security on the situation.
The Goliath ride opened in 2006, and it has an elevation of 200ft (60m), a 170ft plunge, a 540-degree spiral, and a speed of up to 70mph (112km/h), according to the park website. On its "thrill scale", Six Flags ranks Goliath at level four out of five.
Monday's death is the latest of several at the Georgia amusement park, according to personal injury attorneys.
The fatalities include a 45-year-old man dying from an apparent heart attack after riding the Goliath in 2006, said the Doan Law Firm.
Six Flags is the largest amusement park operator in North America, with 20 amusement parks, 14 water parks and nine resorts across Canada, the US and Mexico.
The incident comes just weeks after one of its parks in southern California announced it would close the popular X2 roller coaster after more than 100 people alleged brain injuries from the ride.
Six Flags said the ride had passed a range of safety tests, but that it had decided to retire it because it was "the right thing to do".