Bruno Covas said the city's public hospitals had reached 90% capacity and could run out of space in two weeks.
He accused those who flouted lockdown rules of playing "Russian roulette" with people's lives.
São Paulo is one of the country's worst-hit regions, with almost 3,000 deaths so far.
Brazil's far-right president Jair Bolsonaro has been strongly criticised both at home and abroad for his handling of the country's escalating coronavirus crisis.
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