Police said Jones, 34, then pushed Ragin to the ground. Police eventually determined Ragin was the primary aggressor.
Ragin, who was charged with two counts of battery, was transported to Grady Memorial Hospital to be treated for his injuries.
Ragin works for ABM, a contractor for the airport that deals with building maintenance and facility services.
Jones and his companion declined medical treatment.
Jones, who was drafted in 2005 out of West Virginia by the Tennessee Titans, has also played for the Dallas Cowboys and Cincinnati Bengals. The cornerback played in nine games for the Bengals last season. He is currently a free agent.