A spokesman for Gatwick Express, which is run by Southern railway, said it first received reports about the incident at 5.45pm.
He said: "We have received reports of an incident on board a Gatwick Express train which was en route to Victoria from Gatwick this afternoon.
"The emergency services are in attendance at Wandsworth Common station. We have no further information at this stage."
A spokesman for British Transport Police said the incident was not being treated as suspicious, and that a file is being prepared for the coroner.
Southern Rail tweeted that services between Victoria and Balham were being delayed, saying: "Emergency services dealing with an incident between Balham & Wandsworth Common."
Residents said they were shocked to see the air ambulance land on the common earlier in the afternoon.
One said: "We were coming back across the common when we saw the helicopter land.
"It was at about 6pm. There were lots of police and ambulances there, it was disconcerting."
Another said: "I heard a man was hit by a train and heard the air ambulance land on the common. It's such a horrible thing to have happened."