The incident is believed to have taken place on the forecourt of a petrol station in Stretford on Wednesday evening.
The images were widely shared on social networks.
Greater Manchester police said they were aware of the video and were investigating.
The force tweeted: “We know of a video on social media that shows a man being tasted [sic].
“We are aware of this incident and are investigating. “
Coronavirus in the UK
Andy Burnham, the mayor of Greater Manchester, released a statement on the video.
In the clip, a little boy can be heard repeatedly shouting “Dad” as a man struggles with two officers on the forecourt of the gas station.
One of the officers then said, “You are the source of the problem”, to which the man replies “I am not causing any problems”.
It appears that one of the officers then said “Okay, taser him” moments before the gun was fired.
The man then falls to the ground while the now hysterical child shouts “Dad”.
Some time later, several other police vehicles arrived and the man was handcuffed and taken to the back of a police van.
After images were shared on Twitter, a woman commented that she recorded them in Stretford at 11 p.m. Wednesday and released a second, longer clip of the incident.
Chief Constable Ian Hopkins confirmed that the incident was under investigation by the Independent Office for Police Conduct.
Greater Manchester police then issued a statement.
It read: “A man was charged in an incident which saw a Taser pistol deployed by a GMP officer.
“Shortly before 11:00 p.m. on Wednesday, May 6, 2020, police observed a vehicle traveling safely at high speed on Chester Road in Stretford.
“The vehicle was stopped and the driver, Desmond Ziggy Mombeyarara (12/12/1985) of Cornbrook Park Road, Old Trafford was stopped and charged with the following facts:
· Two counts of resistance to a constable in the performance of his duties
· An excessive speed driving account
· One count of not having automobile insurance
Once you are unable to drive while drinking
· A leader without reasonable excuse to cooperate with a preliminary test
· One count of not stopping when necessary
· A count of unnecessary trips.
“He was placed in pre-trial detention to appear before the Manchester District Court today Friday, May 8, 2020.”