A spooked horse pulling a carriage has bolted across tram tracks on St Kilda Road, throwing its driver from his seat.

The chaotic scene has inflamed calls to ban the sight-seeing carriages popular with tourists in Melbourne's CBD.

The horse was pulling a carriage of six passengers on Princes Bridge towards Flinders Street Station when it took off at 9.30pm on Saturday.

The driver, a man in his 40s, was taken to The Alfred hospital in a stable condition with back injuries.