Romanian television has shown video images, apparently taken by a passenger seated on the right-hand side of the aircraft, which seem to show the 737 experiencing a sudden impact or explosion during its take-off roll.
Images taken after the event show the aircraft off the runway, with evacuation slides deployed and damage to its left-hand undercarriage and engine.
While Tarom could not immediately be reached for comment, local reports cite Tarom director Gheorghe Barla as saying that a vehicle had been unintentionally left on the runway after checks.
The aircraft had been bound for the Egyptian resort of Sharm El-Sheikh.
Snow and fog were present at the time of the accident. Local reports state there were 120 passengers on board, although there is no indication of any injuries.