Witnesses claim the warden was targeted as he confronted drivers parked illegally next to St John’s RC Primary in Portobello at peak drop-off time.
The attack happened in front of shocked parents and children shortly before 9am on Monday when the attendant approached a driver who had parked on yellow zigzag lines in Hamilton Terrace.
The victim did not sustain any injuries but has been left “shaken” by the assault.
Police are investigating reports that the driver drove at the attendant and struck his leg before he fled the scene.
The driver has been described as a white man in his 30s to 40s with a medium build. He was driving an estate-style vehicle.
Sergeant Mark Pickavance said: “This was a distressing incident for the victim, which took place in the presence of a number of young children and their parents right outside a primary school.
“A number of parents witnessed the driver’s actions and have come forward. Positive lines of inquiry are being investigated in order to identify the driver of the vehicle.”
The attack has also sparked condemnation from transport leader Councillor Lesley Hinds, who urged anyone who saw what happened to contact the police.
She added: “Assaulting or endangering the safety of parking attendants is unacceptable behaviour and is not tolerated by the council.
“We would urge witnesses of this incident to contact the police with any information.”
A Police Scotland statement said: “Police in Edinburgh are investigating an assault on a City of Edinburgh Council parking attendant in the Duddingston area.
“The incident happened around 9am on Monday in Hamilton Terrace when a parking attendant approached a driver outside St John’s Primary School who had parked on yellow zigzag lines.
“Officers are investigating reports that the driver then drove at the parking attendant and struck his leg before leaving the scene.
“The driver is described as a white man in his 30s to 40s with a medium build and he was driving an estate-style vehicle. The victim was shaken however did not sustain any injuries.”
Anyone who witnessed the incident or has information has been asked to contact Police Scotland on 101 or Crimestoppers on 0800 555 111.