The accident occurred shortly after 2300 GMT when a train operating between Tunis and the southern city of Gabes derailed near Msaken, a town about 150km from the capital.
The driver and a passenger were killed while 34 other passengers were injured, the SNCFT said.
"An investigation has been opened to clarify the circumstances and causes of the accident and to determine who was responsible," it added.
The accident comes 15 months after a collision between two trains in the south of the capital injured around 100 people.
In December 2016, five people were killed and more than 50 injured in the same area when a train and a public bus collided.
Blamed on faulty infrastructure, the accident prompted the sacking of the SNCFT's then chief executive.
In June 2015, Tunisia experienced one of the worst rail accidents in its recent history when 18 people died in a crash between a train and a truck at El Fahes, about 60km south of Tunis.
Tunisia Train Wreck Kills
Derailed passenger cars are pictured at the scene of a train accident near Msaken, about 150 km south of the capital in eastern Tunisia, on June 21, 2023.
TUNIS — Two people were killed and 34 injured when an overnight passenger train careered off the tracks and overturned in eastern Tunisia on Wednesday, the state-owned SNCFT rail company said.