The bus crashed into the Alexandre III bridge, a tourist magnet due to its ornate structure and views over the Eiffel Tower and River Seine. The Paris fire service said one of the injured was seriously hurt.
The crash came during a large scale event on the Seine to promote the French capital's bid for the 2024 Olympics, with a floating running track installed across the river just next to the bridge.
A police source said the bus was not travelling along its usual route, having been diverted because of the Olympic event.
The Big Bus Tours company, which offers sightseeing trips around Paris on open top buses, confirmed to AFP that one of its vehicles had been involved in the accident, without giving further details.
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