Officials said hospitals had reached 90 per cent capacity.
Businesses, schools and public spaces are shut in the city of 12 million, but many people have been flouting stay-at-home rules without being punished.
São Paulo has reported almost 3,000 deaths from the virus. In the most recent 24 hours 7,938 new cases were reported, taking the total above 241,000.
Only the US, Russia and the UK have higher numbers.
Brazil’s death toll of 16,118 is the fifth highest in the world.