Witnesses told 9News the rider failed to give way to passengers getting off the tram on Swanston Street near La Trobe Street about 2.30pm, leading to the tram driver yelling at him.
The pair allegedly yelled at each other before the argument turned violent.
“It’s understood a tram driver and e-bike rider had a verbal argument, which turned physical,” police said.
Both men were seen with blood on their heads as they were spoken to by police after the incident.
The tram driver, aged in his 50s, was taken to the Royal Melbourne Hospital with non life threatening injuries.
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The rider, who was wearing a Hungry Panda uniform and refused an ambulance, was arrested and is helping police with their inquiries.
Hungry Panda declined to give a statement before it investigated the incident.
A Yarra Trams spokesperson thanked emergency services for their “rapid response” to the incident.
“Yarra Trams will work closely with authorities to support an investigation into the incident,” the spokesperson said.