The incident happened during Monday evening's rush hour at the Rond-point du Prado metro station.
Witnesses said an argument started at around 7pm between the two girls which quickly became violent when the older of the two produced a knife and stabbed her girlfriend twice.
The victim was rushed to hospital and was reported to be in a stable condition.
The girl's attacker fled the scene but turned herself in later that evening. She is being held by police on suspicion of attempted murder.
France Soir reported that the fight had been prompted by jealousy after the older girl discovered that her girlfriend had secretly started seeing someone else.