Mr Kawczynski said he was "appalled and horrified" by the incident, and has spoken to Chief Superintendent Tom Harding.
It comes after a video was shared online showing rowdy yobs shouting, swearing, running up and down the street and dancing to Abba, while several perplexed officers tried to get things under control.
The live video was deleted, but was then reuploaded by Alexandra Titley to show her dismay over the lack of respect for social distancing measures by those involved. It received 15,000 views and a barrage of comments condemning the actions of the yobs.
Mr Kawczynski said: "I am absolutely appalled and horrified. The police have enough on their hands at the moment without having to deal with these delinquents."
"The idea that we are all in lockdown yet these people are out in the street is mind boggling. A lot of people will expect the book to be thrown at these people.
"Meanwhile we have people dying in our hospitals. This behaviour has to be called out and these people have to be punished."
He added: "Thank you Chief Supt Tom Harding for work you are undertaking to keep us all safe at this difficult time. Thanks for listening to me today about this case which I have asked you to investigate very thoroughly. I would like strongest possible fines."