Two of the victims suffered minor injuries, while the third, although more seriously injured, is not in life-threatening condition, police said.
The detained man, whose nationality was not disclosed, attempted to stab at around 8 a.m. at Gare de Lyon, which serves domestic trains as well as trains to Switzerland and Italy.
"The suspect did not shout any religious slogans during his attack," a police source said. Paris police chief Laurent Nunez said the attack did not appear to be linked to terrorism and said the attacker appeared to be suffering from mental health problems.
The area between the first and third halls at the station has been temporarily closed, rail operator SNCF X said in a statement.