The incident happened on Sunday March 13 at around 4pm, when a loud bang was heard by passengers.
Linda Wild, from Whitby, who was travelling in carriage H, said: “We could see a drone on the left-hand side of the train and thought it must be taking photos.
“The next thing we knew there was an almighty crash - it sounded like it had crashed into the roof.”
She added: “It was such a shock and could have caused a major accident. What if it had gone through the window?”
Linda, who was travelling with her husband and some friends, said the rest of the journey was “brilliant” but that the incident had scared her and left her with huge concerns about the use of drones and their safety.
She spoke to an official on the train who said it would be reported to the British Transport Police.
Liz Parkes, head of operations at the North Yorkshire Moors Railway (NYMR) said: “We are aware of a report of a drone grazing the back carriage of the 15.30 60103 Flying Scotsman service from Grosmont on Sunday March 13 in the Huntingbridge area.
“This is currently being investigated by the NYMR and British Transport Police.
“While no damage was caused, obviously drones are distracting to our drivers and could result in a criminal prosecution for endangering trains.
“If any members of the public become aware of any incidents of this nature, we would urge them to report it immediately to a North Yorkshire Moors Railway staff member or the British Transport Police so it can be investigated further.”