“This issue has caused major congestion all around Manchester, we are trying to get it cleared as soon as possible,” Northern said on X.
Other train operators affected include Avanti West Coast, CrossCountry, East Midlands Railway, Northern, TransPennine Express and Transport for Wales, National Rail said.
A BTP spokesperson said officers were called to the line near Levenshulme railway station at about 14:00 to reports of “a person in a precarious position”.
“Officers attended alongside Greater Manchester Police, paramedics and fire and rescue, and a person was arrested in connection [with the incident].”
Northern said tickets from impacted services could be used on Manchester Metrolink services between Manchester Airport and Manchester City Centre, in both directions, until further notice.
A Northern spokesperson said: “All other services in the North West will be at risk of cancellation and disruption due to the severe impacted caused by this incident.
“Customers with tickets to travel on Northern services can travel on board Manchester Metrolink Tram Services, TransPennine Express, East Midlands Railway, Transport for Wales & Cross Country services via any reasonable route until the end of the day.
“This will be the quickest route to/from Manchester City Centre – Manchester Airport.”