A further 38 positive cases were confirmed on Tuesday, giving the town an infection rate of around 122 per 100,000 of population.
Middlesbrough Mayor Andy Preston said it was time to act to halt the spread of the virus and protect people's wellbeing and jobs.
The Council is concerned that in the absence of a local proposal, the government will impose harsher restrictions that would lead to increased isolation and loneliness, particularly for those living alone, and cause long-lasting damage to the town's economy.
Details of the proposal, which is being finalised today, would include:
- A restriction banning people from different households socialising inside homes (with exemptions covering those living alone, support bubbles, childcare and caring for the vulnerable)
- No change to current ‘rule of six' laws in respect of meeting others outside of homes in Covid-secure venues such as cafes, restaurants and pubs
- A request for government funding to allow the Council to increase the amount of local test and trace activity and support communities and businesses
- A request for increased stocks of winter flu vaccinations to protect the most vulnerable
Mr Preston said: "We've thought long and hard about this and I've concluded it's the right thing for Middlesbrough.
"Our infection rate is growing at an alarming rate and Covid has already caused too much damage and pain to families around our town for us to stand by.
"Test and Trace data tells us infection is mainly being spread within households. It's on that basis that we're going to ask government to restrict socialising in homes.
"We've got to try and get a grip of the virus, protect the most vulnerable and keep children in school.
"It's important to stress that people would continue to be able to care for vulnerable relatives and provide childcare where necessary. Support bubbles would also be unaffected.
"There's a balance to be struck here because the long winter months ahead will be lonely for many people. This isn't about people barricading themselves in their homes for months on end.
"We've got to do all we can to get a grip on Covid in Middlesbrough while fighting night and day to tackle isolation, protect people's mental health and keep them in work.
"If we don't make a proposal to government we risk them going further than we think is necessary at this stage and applying restrictions seen elsewhere in the North East.
"That would be brutal for businesses and jobs at a time when we're delivering exciting plans for our town centre.
"I don't want people be banned from meeting a cousin or friend for a coffee or a bite to eat. Businesses can be Covid secure and as a Council we'll continue to breathe down the necks of unsafe venues and promote the places doing their bit."
The Council is to explore supporting more community activities to tackle isolation and loneliness among the vulnerable should the restriction be introduced.
Mr Preston and Council officials will continue to work with representatives from Darlington, Redcar and Cleveland, Hartlepool and Stockton councils in an attempt to provide consistency and clarity across the Tees Valley.