When a DeKalb County, Georgia, police officer apparently put his hand over his holstered gun as he approached White's car, the wide receiver said he grew upset and worried.
White received two traffic tickets but said he wanted to report the officer for his actions.
"... It may save the next black man's life," White wrote.
Police told CNN they are aware of the incident, but White had not filed a report as of Wednesday night, as he tweeted he would. If he does, the matter will be investigated by the internal affairs unit, police said.
White's experience comes during a time of well-publicized traffic stops of African-American motorists who've been fatally shot or treated roughly by police. The incidents have sparked protests and nationwide discussion about the interaction of police officers and minorities.
Recalling the incident
White recounted the incident to CNN at his home Wednesday night.
"I said, 'On a routine traffic stop for a speeding ticket, its protocol for you to get out of our car and put your hand on your weapon and come walk to someone's car?' He told me, 'Yeah, yeah, that's police protocol.'"
"So I was like, 'Are you serious?'" White said the officer told him, "No, that's my protocol, that's what I do as a police officer."
"It was a scary moment for me because at that time I was like anybody else -- I felt vulnerable."
"If something went wrong or if I tried to argue with this guy ... I could've got shot."
White was pulled over in suburban Atlanta and was cited for speeding and an expired license plate. He had no problems with that, the athlete said in a series of eight tweets.
White said he questioned the officer about why the officer felt the need to unsnap a restraint on his holster and grab his gun.
The officer purportedly told him it was police procedure, then clarified that it was his preference.
"It's cops like you that makes this world a very ugly place its a good thing I already had all my information to give him or I could've died on a routine traffic stop cause if u stopping me for speeding I don't see a reason to grab your gun," White tweeted.
When the officer put his hand on his gun, it made White feel like the cop was nervous and White then became more nervous, White told CNN's Coy Wire, who was White's teammate for three years.
Maj. Stephen Fore of DeKalb County Police said a policy manual is posted on the department's website. It doesn't include any mentions of hands on weapons during traffic stops.
Holsters are divided into three different levels, with Level 3 being one many departments prefer. It protects the officer from having his or her gun taken during a confrontation with a suspect because it takes three steps to unholster a handgun. That's the level used by DeKalb County officers.
One expert told CNN that the first thing an officer is looking out for during a traffic stop is his or her safety. A driver should turn off the car, roll down the window, stay inside the car and put their hands on the steering wheel, or at least make it clear that there's nothing in their hands and they aren't reaching for anything.
"The officer doesn't know who you are," Cedric Alexander, CNN law enforcement analyst and public safety director of DeKalb County, said last year.
White told CNN that he intends to file a report on Thursday. He also needs to get his driver's license back.
He told Wire that if it is procedure for an officer to have one hand on his gun, then that is something that needs to be looked into.
Following mom's advice
White was driving a Camaro with tinted windows on Interstate 285, and said he didn't realize he was speeding due to the busy traffic on the four-lane road. He said he followed advice his mother once gave him to get all his information ready and have the window rolled down when the officer approached.
Reactions to White's tweets were mixed, but most voiced support for the police officer's actions. Others said they have experienced the same thing and weren't upset by an officer putting a hand over a gun.
A man named Chris Wright wrote: "Ima have to disagree with you on this. Unless he had it pointed on you. I've been stopped and had a cop unbuckle his strap."
Another man said White, who is black, was unnecessarily making the issue about race.
"I'm white, and everytime I've been pulled over at night, the cop did the exact same thing. Ignorance. Stop feeding the divide," Michael April said, although it is unclear when White was pulled over.
A woman tweeted her support.
"God bless you and stay strong! Tell your story!" Malina Carrillo wrote.
White, 36, played 11 seasons for the Falcons. In 2010, he led the NFL with 115 receptions and was named to the All-Pro team. He was released by the Falcons in March and at this point, midway through the season, it is unlikely he will sign with another team.