The scooter was thrown from an over-bridge on Gartlea Road, Airdrie, North Lanarkshire, at 17:50 on Thursday, landing on top of a train.
The driver brought the train to a halt and later services on the line were subject to delays and cancellation.
BTP said the incident was "incredibly dangerous".
They appealed for anyone with information to get in touch.
PC Mark Harrigan said: "This was a particularly alarming incident for the driver of the service in question and in particular was a great inconvenience to the wider public who were subjected to lengthy delays and cancelled services as a result of this reckless act of vandalism.
"Fortunately no-one was hurt, but trespassing on the railway or risking coming into contact with overhead wires is incredibly dangerous.
"Criminal damage to the railway can result in serious and even fatal consequences for rail passengers, workers and those committing the damage."
BTP would like to speak to anyone who may have seen people acting out of the ordinary or loitering in the Gartlea Road area, adjacent to Halfords and Morrisons petrol station, around the time of the incident.
British Transport Police (BTP) have launched an investigation after a child's scooter was thrown at a train, causing lengthy delays to services.