Olivier Véran said infection rates in the capital and its suburbs are on the rise and a decision to impose further restrictions will be taken on Sunday.
He added that a “total closure of bars” may be necessary in the capital.
France, one of many European countries experiencing an increase in cases, recorded more than 13,000 infections on Thursday.
should serve as a “wake-up call”.
At a press conference Thursday, Mr Véran said the Paris region had crossed three qualifying thresholds for maximum alert on Thursday.
One of these was the number of infections, which has now exceeded 250 per 100,000 population.
“We need a few days to confirm the trends, but if they are confirmed we will have no choice but to put it on high alert, starting on Monday,” he said.
According to Mr. Véran, more than 30% of the beds in intensive care units in Paris are occupied by Covid-19 patients.
He warned that if maximum alert was put in place, there would be no more family reunions and bars would be closed. Bars and restaurants in the area must already close at 22:00.
Similar restrictions have already been introduced in Marseille. Last Monday, Mr. Véran announced that bars, restaurants and gyms would close in the southern city for at least two weeks amid a surge in cases.
France recorded 13,970 cases and 63 deaths on Thursday. More than 31,986 people have died in the country since the start of the pandemic, according to data from Johns Hopkins University.
Elsewhere in Europe, the Spanish government has ordered a partial lockdown of the capital Madrid. Under these restrictions, residents will not be allowed to leave the area unless they are required to take essential travel.
The UK has removed Poland and Turkey from its no-quarantine list. Those arriving from both countries from 04:00 BST (03:00 GMT) Sunday will need to self-isolate for 14 days.
Poland’s infection rate has risen, while the British government has said it has eliminated Turkey over concerns over how the country is reporting its data.