"Movement will be banned on all public roads from 7 pm to 6 am... for two weeks," Madbouli told a Tuesday news conference.
"All mass transport, public and private, will be halted over the same period."
Penalties for violators include a fine of up to 4,000 Egyptian pounds (just over $250) and even prison, he said.
The prime minister said central and provincial government services including the issuing of licenses would be suspended for two weeks.
He said that malls and shops selling more than basic goods would be allowed to open until 5 pm on work days but would be required to close over the Friday-Saturday weekend.
Cafes and nightclubs would be closed, while restaurants and other food outlets would be allowed to offer delivery services only.
Bakeries, grocery stores, pharmacies and supermarkets outside malls would be exempted.
The health ministry has so far registered 19 deaths from the coronavirus in Egypt out of 366 confirmed cases.
The government has already closed schools and universities and halted air traffic in a bid to slow the spread of the coronavirus among the country's 100 million people.
Religious authorities have also shut all mosques and churches and halted prayer gatherings for at least two weeks.