The killings occurred during the night in the Jendouba area, the ministry said in a statement.
Tunisia has been wracked by violence blamed on jihadist groups since the January 2011 Arab Spring revolution that ousted long-time dictator Zine El Abidine Ben Ali.
The statement said a National Guard patrol was sent to investigate reports that a civilian and a prison warden had been shot dead by an armed group at a roadblock set up by armed men in Jendouba.
Security operations were under way to track down the armed group, the ministry said, without giving details.