The incident occurred around 7am on line 1 of the Paris Metro network at the Gare de Lyon station.
The victim, believed to be a young man aged in his 20s, suffered severe burns to the face and the hands and has been left in a critical condition, reports say.
They were treated at the scene by paramedics before being taken to hospital in the French capital.
The substance used in the attack is being examined in a laboratory. A police source told Le Figaro newspaper it was too early to confirm whether the liquid thrown at the passenger was acid.
According to reports in the French press, the acid attack took place during an altercation between two homeless people.
One of the individuals involved is reported to have been covered in blood.
“A rag soaked in a liquid that could well be acid has been found at the scene,” a police source is quoted as saying by Le Parisien.
Police are now hunting for the person who threw the liquid.
The attack follows another incident on Wednesday evening when two people suffered acid burns on line 11 of the Metro.
In this case acid had been poured onto a flip down seat and the floor of the Metro carriage. One person suffered burns to their thighs, while another victim who noticed the bottle of liquid suffered burns to their hands as they tried to move it.
Early investigation findings suggest there are no connections between the two incidents.
Wednesday's incident occurred after the passenger boarded the train at Place de Fêtes station. Both victims were taken to hospital, while the Metro was evacuated at Arts et Metier station so police could investigate.
French police are investigating if the corrosive liquid was left on the seat as a sinister act or by accident.
According to the initial investigation, the bottle contained sulfuric acid.
“The liquid that burned the two passengers is a type of sulfuric acid, this has been verified by the technicians of the central laboratory of Paris,” a police source told LCI media.
There is no evidence at this stage that the two incidents are linked.