Gunmen ransacked the building in the north-west of the country before taking the hostages, Italy’s Ansa agency said.
The area is close to a stronghold of militant Nigerian group Boko Haram.
The attack comes three months after a French priest was released after being kidnapped by Boko Haram in the same region and held in Nigeria.
The latest attack took place in the district of Maroua in the early hours of Saturday morning.
The gunmen were reported to have arrived by car before entering the building where the priests and the nun were staying at around 02:00 local time (01:00 GMT).
The two priests were from the Vicenza region of Italy, the Italian foreign ministry reported.
It says it has set up a crisis unit to work for their release.
Read more: http://www.bbc.com/news/world-africa-26899710