Neighbourhoods have been sealed with a single entry and exit point under the "triple lockdown", which refers to movement of people and vehicles; households with infected people, and clusters where people who have had contact with infected people live.
People have been advised to stay at home and those who go out must carry signed forms declaring why for police inspection. All offices, businesses and public transport have been shut.
The state has made wearing masks and social distancing mandatory for a year, and banned spitting in public.
Violating these rules can result in a fine of up to 10 000 rupees or two years in prison.
Divya Gopinath, a city deputy commissioner of police, said nearly 220 people were arrested in the first two days of the new lockdown and 208 vehicles seized.
Several states have either already introduced weekend curfews and extended existing lockdowns as the situation worsens.
India has more than 740 000 cases, trailing the United States and Brazil, according to a tally by Johns Hopkins University.