Greene was charged with failure to stop/halt/frisk, driving on a suspended license, reckless driving and illegal parking, according to Franklin, Tennessee, police.
According to The Tennessean, Franklin police informed the Titans, who then contacted Greene to tell him that warrants had been obtained for his arrest. The 29-year-old turned himself in at approximately 9 p.m. on Friday, and posted a $2,000 bond. He was released less than two hours later.
"We have talked to Shonn and are aware of the reports," the Titans said in a statement Saturday. "This is not the type of behavior we expect from any member of our organization. We will continue to gather additional information as it becomes available and handle the matter internally."
Despite the arrest, Greene's roster status with the Titans is not in jeopardy, a team source told ESPN.com's Paul Kuharsky.
Greene was approached by a parking enforcement officer Friday afternoon for being illegally parked in a handicapped space in a public square in Franklin, which is located approximately 20 miles south of Nashville.
After ignoring the officer's request to see a handicapped placard, Greene entered his BMW and sped away from the scene, nearly hitting the officer in the process, according to Franklin police.
"Greene showed no regard for the parking enforcement officer's safety, or the safety of others, as he recklessly evaded the parking enforcement officer over what would have been a simple parking ticket," the Franklin Police Department said Saturday in a news release.
Although he was forced to stop due to traffic, Greene sped off again when he was approached a second time by the parking officer, according to The Tennessean.
"The entire situation could have been avoided if he would have left that handicap space for who it was intended for," Franklin police sergeant Charles Warner told the newspaper.
"The fact that he didn't and got caught being parked there, he could have stopped things from going any further than a parking ticket if he would have simply communicated with the parking enforcement officer and not taken such evasive measures to get away from her, increasing the seriousness of what would have been a simple parking ticket."
Greene's court appearance is scheduled for Nov. 13. The six-year veteran is in his second season with the Titans, who signed him to a three-year contract prior to the 2013 season. He has missed the last two games with a hamstring injury.
Greene is listed as probable for Sunday's game against the Texans.
ESPN.com Titans reporter Paul Kuharsky contributed to this report.