The Nottingham-born actress told The Graham Norton Show the incident happened in 2015 after a ceremony in the city to unveil the tram.
She said she and her mother had been told they could have a free ride but were later challenged by a conductor.
Nottingham Express Transit said it was an "unfortunate misunderstanding".
McClure is among several well-known locals to have trams named after them on the Nottingham city network.
Others include ice skaters Jayne Torvill and Christopher Dean, cricketer Stuart Broad and author DH Lawrence.
Speaking about the incident, the actress said attempts to prove who she was fell on deaf ears at the time.
McClure said: "We unveiled the name and then I got on the tram with my mum because we were doing Christmas shopping and they'd said 'we'll give you a free ride'.
"We were pulling into our stop and I can see the ticket man coming towards us and he's like 'can I get your ticket?'"
She said the conductor was unswayed when she presented the plaque she had received at the ceremony and ordered the pair off.
"I was like 'oh my god - you've thrown me off the tram for fare evasion. I was mortified," she explained.
Despite the misunderstanding, McClure said she wanted her name to stay on the tram for good.
Nottingham Express Transit, which runs the network, said: "This was an unfortunate misunderstanding as the travel officer was unaware that Vicky had been offered free travel on the day the tram was named in her honour.
"As you would expect from her, Vicky took the matter in good part and the situation was soon resolved.
"We apologised to her as soon as we were aware of the confusion and we certainly didn't want to spoil such a special occasion."
Line Of Duty star Vicky McClure has revealed she was ordered off a tram named in her honour after being accused of fare evasion.