The extremist group made the claim through its official news agency.
A man shouting "Allahu Akbar," (God is great) stabbed the two women before French soldiers gunned him down.
Police shut down and sealed off the station and French Interior Minister Gerard Collomb immediately went to Marseille.
French prosecutors have opened a counterterrorism probe, but Collomb has not yet formally declared it a terror attack.
Police video is said to show the suspect stabbing one woman, disappearing, and re-emerging moments later to attack his second victim.
He ran straight toward soldiers who opened fire and killed him. The attacker and his victims have not been publicly identified.
French President Emmanuel Macron tweeted that he is "deeply outraged" by the "barbarous" attack while praising the swift but cool-headed response by the soldiers.
France has been in a state of emergency since November 2015 after Islamic extremists attacked a concert hall in Paris and attacked several restaurants and bars.
Ten months earlier, gunmen opened fire in the offices of the satirical cartoon magazine Charlie Hebdo and later seized hostages in a kosher supermarket.
There have been several other terror attacks in France since then, including on in Nice where 86 people died when an attacker driving a truck ran down pedestrians celebrating Bastille Day in July, 2016.