Services are being diverted to alternative stations.
NWAS said three ambulance crews and a critical care team in an air ambulance were treating four people at the scene, including one with suspected serious injuries.
The free city centre bus has been suspended until further notice.
TFGM warned the crash could also disrupt travel to the Peter Kay performance at the AO Arena later.
TFGM’s Fran Wilkinson added: “This is a serious incident which is currently ongoing.
“Our staff are continuing to support emergency services at the scene, while also assisting members of the public.“
“Piccadilly Gardens will be closed for some time, and we are expecting bus and Metrolink services to be impacted throughout the afternoon and into the evening.”
A Greater Manchester Fire and Rescue Service spokeswoman said firefighters had used specialist cutting equipment to remove someone from the bus following the crash.
