State TV ERT said Mr Papademos and his driver were both "seriously hurt" and rushed to a nearby hospital.
"We are shocked. I wish to condemn this heinous act," media minister Nikos Pappas told the station.
ERT said Mr Papademos, Prime Minister from 2011 to 2012, had been targeted by a letter bomb.
A police source said a number of people had been hurt but could not say if Mr Papademos himself was in the car at the time of the blast.