The Sports Bar on Portland Place had its licence suspended for four months from today at a meeting of the city's licensing board.
Councillors heard police were called three separate times to noise complaints after closing time.
In one of the incidents, officers say reinforcements were called after staff at the bar were "confrontational".
It is understood that former Lib Dem councillor Mr Ponton owns the bar alongside other family members, but he is not actively involved in its day-to-day running. He did not wish to comment on the case when approached by the Evening News.
It is not the first time that Mr Ponton's bars have been in trouble with licensing officials. In 2002, he was fined after under-age drinkers were found within his Oz Bar on Candlemaker Row.
Licensing leader Marjorie Thomas – a former colleague of Mr Ponton during his time as a Liberal Democrat councillor – left the room for the discussion because she said she "knows the people involved" and said it would be "inappropriate" for her to chair the discussion.
SNP councillor Norman Work, who took over as convener in the absence of Cllr Thomas, said: "We have to get the message out that pubs in Edinburgh have to be managed properly. We decided to suspend for four months."
During yesterday's meeting, Inspector Gordon Hunter, from Lothian and Borders Police's licensing department, said officers visited the bar at 1:50am on 11 October following a complaint.
"Numerous intoxicated persons were seen leaving the venue," said Inspector Hunter. "The shutters were down, the doors were locked and there was loud music and voices from within."
When licensing officers made enquiries, Mark Hartley identified himself as being in charge, and officers reported that he was "intoxicated".
Officers are said to have received a "confrontational" response from him and had to withdraw from the bar and call for additional police assistance, with ten officers attending.
Further noise-related complaints were also made on 1 November and 22 November.
Alistair Macdonald, solicitor for "The firm of Ponton, Ponton and Ponton", which consists of Thomas, Isobel and Ian Ponton, said Mr Hartley had not told the owners about the incident immediately and was dismissed within a day of them finding out.
Mr Macdonald told the licensing board: "The background is that there was an incident, but we would hope you would accept that it was without the knowledge of the owners or premises manager.
"Police are proposing increased vigilance by management to make sure things don't happen again, rather than saying this is the fault of the owner and management.
"Realistically, is this likely to happen again? I would say, in view of the actions already taken, what's needed is greater vigilance."
He added: "The Pontons are horrified about what happened in their premises."
After the meeting, Cllr Work said: I know that they sacked the person involved but it should be managed better in the first place – and that was the unanimous view of the board."
The bar was due to be closed from today unless a last-minute appeal was lodged.
In May 2002, Mr Ponton – then a Tory councillor – was fined 200 after admitting allowing a 15 and a 17-year-old to be served in Oz Bar. Police had raided it while his son Ian was in charge.