A Metrolink driver reported a collision involving a tram and a pedestrian at about 19:45 BST on Sunday, Transport for Greater Manchester (TfGM) said.
A 31-year-old woman is being questioned in police custody.
The woman arrested was not the tram driver, police confirmed.
Metrolink customer director Stephen Rhodes said he was "absolutely devastated" to hear someone had died.
Greater Manchester Police (GMP) said the man died at the scene.
There was disruption to services on the Bury line for several hours affecting those attending Parklife festival.
Metrolink issued a walking map to help those travelling from the festival at Heaton Park return to the city centre.
Parklife finished at 23:00 on Sunday. The three-mile walk should take about an hour.
Some people questioned the advice on Twitter, suggesting telling young people to walk the distance in wellies in the dark was "unbelievable".
Others said they thought there would be safety in numbers.
Metrolink tweeted there was an "ongoing medical emergency" and advised passengers to avoid Manchester Victoria station.
In a statement, Mr Rhodes, added: "My immediate thoughts are with this person's family and friends.
"As this is now a police investigation it would not be appropriate for me to make any further comment about what happened at this time."
He encouraged those who were able to walk to do so and said 100 buses were also in place, adding: "I'd ask everyone to please bear with us and be patient."
Metrolink said "a good service" was in operation on all lines on Monday and trams were operating in and out of Victoria.
A woman has been arrested on suspicion of murder after a man was hit by a tram and died at Manchester's Victoria station.