A "smart" lockdown was imposed in three localities of Karachi's District Central on Wednesday evening.
According to a notification by the home department, the areas to go into lockdown are Gulberg, North Karachi and North Nazimabad.
The lockdown will remain in effect till May 5.
In the affected neighbourhoods of the three localities, there are a total of 13 patients, the notification said.
The home department said that it will be mandatory for all citizens in these areas to wear a mask and unnecessary movement outside homes is prohibited.
All traders and businessmen will have to keep their shops and offices closed.
There is also a ban on pillion riding in the areas.
Families will not be allowed to keep large gatherings. Those families which have a coronavirus patient they are caring for at home will have to remain under quarantine.
The home department said that the needy people in the areas under lockdown will be provided food supplies by the government.
The move follows a warning by Sindh health minister, Dr Azra Pechuho, who in a video message said that the UK coronavirus variant has arrived in Karachi and was found in 50% of the samples that underwent genome testing.
Dr Pechuho said that the UK coronavirus variant "spreads very fast" and after having already spread in Khyber Pakhtunkhwa and Punjab, leading to the deaths and infections of numerous people, it has now reached Karachi.
She said that owing to it being the month of Ramadan and the Eid-ul-Fitr festival approaching, a lot of people were getting out for shopping. She said that at such a dangerous time when the UK variant is spreading, it is of the utmost importance that safety precautions be taken.
"Do follow SOPs and do not leave your homes unless absolutely necessary," said the health minister.
She warned people to keep away from crowds, wash their hands with soaps frequently, wear masks, and maintain social distancing.
"This way you can protect yourself, your relatives and family and members of the community."
Dr Pechuho encouraged people over 50 to walk in and get themselves vaccinated to protect themselves from COVID-19. "Our vaccination centres are open and remain open after iftar as well," she said.