Health officials said the patients - two Czechs and an American student who studied in Milan - showed mild symptoms. Two were in Prague and the third in the city of Usti nad Labem, 90 km (56 miles) north of the capital.
Vojtech warned against unnecessary travel to regions in northern Italy that have seen the highest number of cases in Europe.
"We ask everyone to very seriously consider not traveling to those (affected) regions for holiday or ski trips unless necessary, because the danger exists," Vojtech told a televised news briefing.
The Czech Republic is the first of its central European neighbors to report coronavirus cases although it joins a list of others in Europe battling the spread of the virus that has infected more than 80,000 since first appearing in China.