Shropshire Council and West Mercia Police said they have received reports of people in the Harlescott, Sundorne and Kynaston Road areas not complying with social distancing guidelines.
Residents have expressed concerns about people congregating in large groups and the council's Community Reassurance Teams will be joined by police to undertake regular patrols of north Shrewsbury in the coming weeks.
Inspector David Bettison, Shropshire's lead for Covid-19 with West Mercia Police, said: "While we know that many people are keeping to the Government guidelines, there are still a number of people who are completely ignoring them. Not only does that pose a risk to themselves but to their families and the wider community.
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“We cannot afford to be complacent and we won’t hesitate to use our enforcement powers.
“We have issued a number of fines already, and we are prepared to enforce the rules if need be.
"If we come across people not adhering to lockdown, this includes people socialising in each other’s homes, more than two people from different households gathering together outside, and those who refuse to wear masks when required to do so, they will be fined.
“We all have a part to play in keeping each other safe, so please do keep following the legislation to help stop the spread of coronavirus and save lives.”
Harlescott's Shropshire councillor, Ioan Jones, added: “This news is concerning, especially when you consider the rising cases across Shropshire.
“I know many people now are well and truly suffering from Covid-19 fatigue, but it is reckless of some residents to congregate in big groups.
“Ultimately, these people are going to be spreading and carrying the virus and passing it on to more vulnerable groups that could lead to more deaths in the long term.
“We are asking people to use their common sense, stay at home as much as possible and limit your contact with people outside your household and support bubbles.”