Officers were called to the property in Shandwick Place at around 10.20pm on Thursday following reports of a large gathering.
One eyewitness told The Scottish Sun that they saw at least two police vans at the scene.
A police spokesperson said: “Police were called around 10.20pm on Thursday, 15 April, 2021 following the report of a breach of coronavirus regulations at a property in Shandwick Place, Edinburgh.
“Officers attended and three men aged 32, 34, and 37 were arrested and charged in connection with the incident and are due to appear at court at a later date.
“There were a further 12 fixed penalty notices issued.”
Meeting other households indoors is still banned in Scotland in a bid to stop transmission. Currently, 20 people are able to attend funeral services but wakes are not allowed. They will be permitted, with up to 50 people, when restrictions are eased under level 3 of lockdown easing - hopefully on April 26.
Meeting other households indoors in private dwellings will only be allowed once authorities move into level two of lockdown easing, which it is hoped will happen on May 17.
People can now meet up in groups of up to six people from six different households - but only outdoors while maintaining social distancing. Coronavirus travel restrictions have also been eased following an announcement earlier in the week by First Minister Nicola Sturgeon.