The girl was taken to hospital after the incident close to the Manchester Art Gallery on Saturday morning, but later died from her injuries, Greater Manchester Police (GMP) said.
Police said they were expecting the streets surrounding St Peter’s Square to be closed for a significant period, as officers attended the scene and sought to establish the circumstances around the crash.
The child was a pedestrian and was not travelling in either the tram or van in the incident in Mosley Street on Saturday morning.
A three-year-old girl has died after a crash involving a tram and a van in Manchester city centre.
"No arrests have been made and inquiries are ongoing," the force said.
