A teenage boy has been arrested after a car struck a pedestrian near the Melbourne Marathon route on Sunday.

The 16-year-old was allegedly driving a stolen Ford Escape east along the tram tracks on Flinders St when he struck a woman at the intersection with Elizabeth St about 10.45am.

Police said the boy failed to stop and made a U-turn outside Flinders Street Station before continuing along Flinders Ln, where he is believed to have struck several unoccupied parked cars.

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The woman, aged in her 50s and from Southbank, was taken to the Royal Melbourne Hospital with upper body injuries. 

She was in a stable condition.

The incident unfolded near the route of the Melbourne Marathon Festival, as more than 60,000 runners took part in the event. 

The boy, from the Greater Dandenong area, was arrested a short time later on Beaconsfield Pde in Albert Park.

He is expected to be interviewed by police. 

Police allege the Ford Escape was stolen from a business on Luster Circuit in Cranbourne South about 2am on Sunday.

Police confirmed the incident was not being treated as an act of terrorism or a targeted attack.