Councillor Tahir Malik said he regrets his actions and would like to "sincerely apologise" after going to a function when coronavirus remains a "real and serious threat".
Luton Council received a "number of complaints" after three councillors were spotted at an event.
It confirmed a new mayor would be appointed at a full council meeting in September.
Following his resignation, Cllr Malik said: “Once again I regret my actions which were below the standard of my position and would like to sincerely apologise to the people of Luton for attending this gathering which was in breach of Covid-19 lockdown restrictions. There is no excuse for what I did – I should have known better and I accept full responsibility for my actions.
“I felt it was important for the disciplinary process – both at the council and within the Labour Party – to determine the outcome and the punishment for my actions, but after reflecting with my family over the last few days, we agreed that the best thing I could do for the town was resign from my position with immediate effect."
Speaking about his role over the last 15 months he said it has been a "great honour to hold this office" and meet thousands of inspiring people.
“I have learnt a valuable lesson from this, but I hope the consequence of my actions serves as a reminder to the people of Luton of the importance of following the Covid-19 guidelines as it remains a real and serious threat," he added.
“My departing wish is to see our fantastic town and our communities pull together to beat this dreadful disease. We should continue to support, be kind and care for one another and recognise the way that people from all walks of life, faith and background have stepped up to help others during this crisis. The strength of the love and compassion in Luton’s communities will always outweigh the minority who will try to divide us."
Cllr Tahir Malik has today stepped down from his role as Mayor of Luton after breaking Covid-19 guidelines. A new Mayor will be appointed at the Full Council meeting on 29 September, who will serve for the remainder of the municipal year. See statement https://t.co/kCfmsCnj5r— Luton Council (@lutoncouncil)August 5, 2020
Cllr Hazel Simmons MBE, Leader of Luton Council, added: “I would like to thank Cllr Malik for his service as Mayor of Luton. He made a mistake which he deeply regrets, and I know he and his family are really hurting right now.
"Prior to this he had been an excellent ambassador for the town both locally and nationally, raising a lot of money for charity during the process. What has happened is unfortunate, and I think it is right for him to step down at this time, but it’s important to recognise the fantastic contribution he has made to Luton.”
A council spokesman said a number of complaints has been received about three councillors who attended a function during the pandemic.
The local representatives admitted to taking part and the complaints will be "addressed through the Council’s Standards Process, in line with legislation".