Both the cyclist and motorist received police warnings following the incident.
Video footage from rider David Brennan’s cycle cameras appear to show the car passing close to him after he undertook the vehicle in a line of traffic in Balmore Road, just north of Glasgow.
It showed Mr Brennan shouting at the unnamed driver and hitting the car’s bonnet before the driver got out of the car and came towards him.
Campaign group Cycling UK said Mr Brennan, 47, from Torrance in East Dunbartonshire, was cycling to work in Glasgow in October 2019 when the incident happened.
It said that after he passed the footage to Police Scotland, officers issued the driver with a written warning, but Mr Brennan received one too.
Mr Brennan said: “I thought I was in danger and reacted to a fast-approaching vehicle by slapping the bonnet with the palm of my hand.
"The driver got out and was incredibly aggressive, hurling abuse at me.
"He pushed me and then punched me in the face.
"I was left with a swollen lip and in a state of shock.”
Jim Densham, Cycling UK’s policy and campaigns manager in Scotland, said: “Dangerous incidents reported to the police on the road must be dealt with fairly and they must recognise that people who cycle are vulnerable road users.”
The body has called for a commitment from Police Scotland to prioritise road traffic enforcement where vulnerable road users are at greatest risk.
It also wants improved guidance to ensure the force deals with reports from vulnerable road users in a “consistent and appropriate way”.
A single “easy-to-use” camera footage submission system is also sought.
Chief Inspector Lorna Gibson, Police Scotland area commander for East Dunbartonshire, said: "Following a review of all available footage and witness testimony two men, 47 and 37, were issued with a recorded police warning following the incident.
"No complaint about the police action has been received by the service."
Chief Superintendent Louise Blakelock, the force’s head of road policing, said: “We regularly conduct road safety operations to improve driver behaviour, educate motorists and other road users, as well as carrying out enforcement activity where required.
“Throughout the summer, officers conducted Operation Close Pass at locations across Scotland to promote the safe use of shared road space.
"During the coronavirus pandemic we have seen an increase in the number of people using our roads for cycling.
"Now more than ever, we urge motorists to give cyclists, and other vulnerable road users plenty of space.”
A Scottish Government spokesperson said: “We are clear that all road users, including cyclists, should feel safe travelling at all times.
“The investigation of alleged offences and decisions about possible penalties or prosecution in each case are entirely a matter for police and the Crown Office & Procurator Fiscal Service, who act independently of government ministers.”