Order already applies to Greater Manchester, other parts of Lancashire and West Yorkshire, as well as Leicester.
Matt Hancock said "some, but not all" restrictions would be lifted from July 24.
The city in the East Midlands has been in a localised lockdown since June 30.
Baroness Dido Harding said the alternative system, which aims to identify where a patient caught Covid-19, is being trialled in Leicester.
It comes amid claims workers were being paid less than the minimum wage and operating without social distancing in the locked-down city.
The East Midlands city is the site of the UK's first "local lockdown". Many believe poverty is to blame – but some have used the crisis to spread racist views.
It's understandable that parents are worried, but trust your children's schools, say the experts.
Boris Johnson’s ‘doers’ v ‘ditherers’ charge is a dangerous one to make.
A spike in coronavirus cases has put Leicester under a local lockdown, with the majority of new cases in the north and east of the city.
Labour leader strongly criticises prime minister in speech to council leaders.