The prosecutor's office said the attack was not politically-motivated.
“It's a common law assault,” said prosecutor Xavier Tarabeux.
A fourth person suffered leg wounds from bullet fragments, police said, adding that they had opened fire on the assailant when he threatened them with a weapon.
The knife attack occurred in the afternoon on a busy street in the centre of the city, the second largest in France.
In October 2017, a man wielding a knife killed two women at the Saint Charles main train station in Marseille in an attack later claimed by the Islamic State group.
The assailant was shot dead by soldiers on patrol to guard against such terrorist attacks.