There have also been reports of similar situations arising in East Lothian.
Under the rules of Phase 1, food and drink outlets are allowed to open, but only for takeaway service.
Police were called to the Canny Man’s in Morningside, the Torfin Bar in Corstorphine and the Old Chain Pier in Newhaven on Saturday afternoon.
Officers were also sent to the Iona Bar on Easter Road on Sunday.
Paul Waterson, spokesperson for the Scottish Trade and Licensing Association, said: “The guidance is quite clear, there’s absolutely no opening until the government allows it.
“The Scottish government will make the decision on that, and no one should be opening any beer gardens before that decision is made. There has been no confusion about that.
“We understand it’s difficult, but we would urge all license holders to go with the government advice.”
Video footage shared on social media shows a crowd of people drinking takeaway pints and sitting in groups outside the Iona Bar on Saturday afternoon.
A local resident who took the video, who wished to remain anonymous, said some of the drinkers directed verbal abuse at her while she was filming.
A passer-by said: “There were probably about 40 to 50 people gathered there when I walked past.
“They certainly weren’t social distancing, a lot of them were just mingling with each other and drinking as if they were at the pub.
“I saw a couple of people filming and a few men started to get quite verbally aggressive.
“I understand someone had reported them to the police.”
Under Phase 1, people are allowed to meet outside with one other household, in a group of no more than eight.