Network Rail Scotland announced the incident shortly before 3pm on Monday and said that the line was closed because of the risk that the vehicle may fall onto the tracks below.
It said it was working with emergency services, including the Scottish Fire and Rescue Service (SFRS), to safely remove the road vehicle from the embankment.
ScotRail has updated travellers saying that the incident doesn’t impact its services to or from Aberdeen, but it does affect services between Edinburgh, Perth and Inverness.
A SFRS spokesperson said: “We were alerted at 2.18pm on Monday, November 15, to reports of a vehicle on the railway embankment near the B937 south of Cupar.
“Operations control immediately mobilised three fire engines and a heavy rescue unit to the scene where they are working alongside Network Rail and emergency service partners."