Police were called after the incident at Dartmouth Street at around 12.20pm.
Video footage appears to show a young man involved in a heated exchange with the conductor, before walking out of the open tram doors.
However, in the footage, he can be seen re-entering the tram amid shouting.
While passengers attempt to keep distance between the conductor and the passenger, he manages to put the conductor in a headlock.
A spokesperson for British Transport Police said: "BTP received a report of an assault on board a tram today (26 July) at Dartmouth Street.
"The incident is believed to have taken place at 12.20pm. Enquiries are ongoing."
