Czechs will also be barred from travelling to those countries, and to and from and other countries deemed risky, effective from Saturday (2300 GMT on Friday).
The full list includes other EU members Italy, Sweden, Norway, France, Netherlands, Belgium, Spain and Denmark, and also Britain, Switzerland, China, Korea and Iran.
International public transport vehicles with more than nine seats will also be banned from crossing borders.
Under a state of emergency declared for 30 days, the Prague government also banned international passenger transport, but kept freight business open.
Babis told a news conference the government would also ban public events of more than 30 people and impose closures of places such as sport centres, spa services and galleries.
Restaurants must close by 8 p.m. and refreshments at shopping malls will be banned altogether.
"It is clear there will be economic impacts. But now we have to do everything for the virus not to spread, to avoid having it here without control," Babis said. "If we see the measures do not have sufficient effect, we will take more."
Some border crossings were to be shut while others would be manned by police. Exceptions will be given to foreigners with residency in the Czech Republic and to cross-border workers.The Czech Republic reported 96 cases of the coronavirus on Thursday. There have been no known deaths from the disease in the central European country.