The shocking incident, which was caught on CCTV, happened around 8pm at the Metro station Edgar Quintet in the 14th Arrondissement of the capital.
According to Le Parisien newspaper images from a video surveillance camera showed the man calmly descending the steps to enter the station, which is on line 6.
The 38-year-old man showed no signs of being agitated and gave no clue that he was about to commit a frightening act of aggression against a random woman.
As the woman waited by the edge of the platform for the next Metro train to arrive the man pushed the woman with both hands onto the tracks before walking calmly along the platform.
Luckily the shocked victim was not injured and she was quickly able to scramble back onto the platform as train pulled into the station on the opposite platform.
Visibly shaken she helped by fellow travellers and then emergency service staff.
The man who pushed her was arrested a few minutes later. According to Le Parisien newspaper a psychiatric examination did not reveal any mental disorder that might have explained his act.
He was however already known to police for other acts of violence, but offered them no explanation for why he pushed the woman.
In 2010 a man was killedwhen he was kicked into the path of Metro train as it pulled into the station in Paris. AFP reported at the time that it was the third such incident in a year.
The 52-year-old was attacked by a traveller standing behind him and was hit by the train as it rolled into the Gare de Lyon station in the early morning rush hour.
The train pushed the man back onto the platform. He suffered severe head injuries and though rescuers raced to the scene the man died 15 minutes later.
In a separate incident a 40-year-old mentally ill man grabbed a young traveller by the waist and threw himself on the tracks at the Bibliotheque Francois Mitterrand station. The two men were killed by a train.
And in APril 2009 a homeless person pushed a commuter off the platform at the busy La Defense station, causing serious injuries. Police tracked down the attacker after viewing footage from video surveillance cameras.
Paris metro operator RATP reacted by installing glass panels along the platform of some metro lines to improve safety.
In September last year The Local reported how a man was jailed for 15 years for a fatal push on a woman at a Metro in the capital.
The death of Vy-Anh Nguyen had left France shocked and prompted the then President Nicolas Sarkozy to talk about the affair during his New Year’s day speech in January 2011.
Frederic Magave-Marques shoved Nguyen down the stairs at Edgar Quintet station after trying to rob her of her mobile phone.