Conte said two Chinese tourists who were visiting Italy had contracted the virus, according to Italian news agency ANSA.
He added that authorities were conducting checks on the journey of the two people, in order to prevent them spreading the virus further.
The patients are reportedly in good condition.
Conte suspended air travel between Italy and China following the announcement.
“As far as we know, we are the first country in the EU to adopt such a measure,” he said.
Italy is the fourth European country, after France, Finland and Germany, to have confirmed cases.
The announcement comes after an Italian cruise ship was placed in total lockdown on Thursday due a suspected case of the deadly virus.
The case was confirmed false late on Thursday.
Samples taken from a Chinese couple were sent for testing after three doctors and a nurse boarded the Costa Smeralda in the port of Civitavecchia, near Rome, to tend to a woman running a fever, local authorities said.
The passenger was a 54-year-old woman from Macau who had boarded the ship on January 25 in the port of Savona.
She came down with fever and flu-like symptoms.
Both she and her partner were placed in an isolation unit on the ship.
The Costa Smeralda departed from Savona in northern Italy and stopped in Marseille, Barcelona and Palma de Mallorca before reaching Civitavecchia.
It had been due to sail for La Spezia in north Italy late on Thursday, before the lockdown occurred.
“We did all that we needed to do,” coastguard commander, Vincenzo Leone, was quoted as saying by ANSA.
“The situation is under control and at the moment it does not seem like there are any reasons for concern on board.”
The cruise ship company, Costa Crociere, released a statement saying its priority was “to guarantee the health and safety of guests and crew” and that it would “strictly comply” with regulations from health authorities.
China reported its biggest single-day jump in novel coronavirus deaths on Thursday, as global fears deepened with at least 18 countries confirming infections.
The World Health Organization (WHO), which initially downplayed a disease that has now killed 212 people in China, was preparing to meet on Thursday to decide whether to declare it a global emergency.