The driver of the Renault Master van was arrested in a third location, the scenic Old Port area of France's second-largest city, David-Olivier Reverdy of the Alliance police union said.
Police tweeted that an operation was underway and asked residents to avoid part of Old Port. BFM-TV said a witness noted the license plate of the van and was able to give it to police, allowing them to make the arrest.
A man was injured at the first bus stop and the woman killed at the second, Reverdy said. The two bus stops are about 5 kilometers (3 miles) apart in the northern part of Marseille.
A motive was not immediately known.
Reverdy said it was too early to blame the incident on terrorism, but "given the times" it could not be excluded as a possible motive. He said all possibilities were being studied.
The incident comes just days after back-to-back van attacks in Barcelona and Spanish resort town of Cambrils killed 14 people.
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