On Tuesday morning, Leicestershire County Council published a map of the lockdown area including the majority of the city itself and parts of Leicestershire that touch on the city's boundaries. The city has recorded 866 of its 2,987 Covid-19 cases in the last fortnight.
The government will review whether it can lift any of the measures in two weeks' time, the health secretary said.
Mr Hancock said: "We can take further action if we need to and put in place more stringent legal controls but I hope that we don't have to because I hope the people of Leicester will follow the social distancing as necessary".
"We do not take these decisions lightly but with the interests of the people of Leicester in our hearts".
While many places in England are preparing to ease restrictions on pubs and restaurants, a rise in coronavirus cases has forced Leicester to impose stricter restrictions this week, with schools closing on Thursday and non-essential shops to be shut for the next two weeks.
Some schools had already closed prior to the local lockdown.
Mr Hancock said the measures will apply not just to the city of Leicester but also "the surrounding conurbation including, for example, Oadby, Birstall and Glenfield".
Leicester mayor Sir Peter Soulsby criticised the slow response from the Government and Public Health England (PHE) in sharing case and testing data for the city.
He said the measures would be enforced by police "in some cases".
Leicestershire Police said: "This is a dynamic situation and we will adjust accordingly, providing proportionate policing under the relevant legislation to help keep people safe in Leicester, Leicestershire and Rutland".
Another commenter claimed the only way it could work was if "armed guards" surrounded the city and suggested that people who worked outside of the lockdown area may face a dilemma.
It came as Prime Minister Boris Johnson thanked the people of Leicester for their "forbearance" in dealing with the new coronavirus restrictions.
"We have had a huge dialogue with the authorities about the concept of neutral venues", Masters told MPs at a Digital, Culture, Media and Sport (DCMS) committee evidence session on Tuesday.
"If that were to happen in multiple areas or the virus creates other risks then obviously there is that risk that we might not be able to complete the season", he added.
Mr Hancock said the Government is "still getting to the bottom of" the reasons why the outbreak in Leicester has occurred.
Sees 15 new cases of COVID-19
Four more COVID-19 cases in Bureau County have been recorded on the Bureau, Putnam, Marshall County Health Department. Preliminary investigation likely connects this person to a known case from a large event in another county.
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