ATG, which runs the Playhouse, has insisted extensive plans had been put in place in an attempt to curb anyone disrupting the record-breaking comic’s performances.
The company revealed Bridges is touring with his own team of security guards who try to spot potential trouble-makers and have them ejected.
And it insisted a “zero tolerance” approach was taken over any bad behaviour at the five shows, which were sold out months in advance.
Hundreds of angry fans have taken to social media to complain about the level of heckling of Bridges at the 3000-capacity venue.
According to eye-witness accounts, Bridges appeared frustrated with the near-constant heckling and angrily confronted some audience members.
There have also complaints on social media about drunken behaviour from audience members at the shows.
Bridges - who is in the midst of an extensive UK tour - has suffered regular problems with hecklers at his live shows in recent months.
He cut short a show in Derry in July after repeated heckling by a female audience member and later donated the takings of the gig to charity.
Ironically, it was a performance at the Edinburgh Playhouse - on Michael McIntyre’s Comedy Roadshow - that propelled Bridges into the limelight six years ago.
A spokeswoman for ATG said: “As a responsible large-scale venue, the Edinburgh Playhouse had several measures in place to manage audience behaviour that were agreed in advance and in partnership with Kevin Bridges’ management.
“Locally-based security personnel, together with Kevin’s own security detail, assisted our staff in monitoring and managing audience behaviour, ejecting anyone who continued to heckle or interrupt the show for Kevin Bridges and the vast majority of the 15,000-plus well-behaved audience members who saw the shows.
“In addition, the Playhouse conducted bag searches on entry, confiscating any contraband alcohol and refusing entry to any patrons who appeared intoxicated.
“The Playhouse has received a limited amount of correspondence in relation to this matter, including praise for the theatre’s zero tolerance approach to instances of poor behaviour.
“Feedback from audience members and managements alike is constantly reviewed to ensure the best possible experience of visiting the Playhouse and we look forward to welcoming Kevin Bridges back for a future sell-out run here in Edinburgh.”
The problems at Bridges’ Playhouse gigs prompted The Stand Comedy Club, which gave the comic his break as a complete unknown at its Glasgow venue, to issue a lengthy statement outlining its own long-time tough stance over audience disruption.
A spokeswoman for The Stand said: “We do not allow heckling at The Stand, which is one of the reasons why big names like Kevin Bridges, Frankie Boyle and Stewart Lee still like coming to play in our relatively small venues.
“We may not allow heckling in our clubs, but the comedians who work here also gig in plenty of clubs where heckling is allowed, and 99.99 per cent of the time, the stories they tell are about idiots ruining shows.
“This is what the vast, vast majority of heckling is - someone (usually drunkenly) embarrasses themselves and makes everyone in the room cringe.
“Generally the person will then try to save face by continuing to heckle in the hope that they will strike gold, while the act on stage and everyone else in the audience wishes with all their might that they would just shut up.”
Bridges’ management company, Off the Kerb, said the comic did not want to comment on the issue.