The incident involved a light engine and a stationary passenger train which was waiting at Grosmont Station this morning.
RAIB inspectors have been sent to the heritage line.
A spokesperson for the North Yorkshire Moors Railway said: "We can confirm that there was a collision at 10.32am today between a diesel locomotive and a stationary set of carriages at Grosmont Station. All passengers were taken off the stationary train and transported back to Whitby; there were no serious injuries reported. As with all such accidents, it is currently being investigated by the RAIB; we have no further information at this time."
A spokesperson for the Rail Accident Investigation Branch said: “The RAIB has sent a team of inspectors to Grosmont Station on the North Yorkshire Moors Railway, where a low speed collision has occurred in a platform between a light engine and a stationary passenger service. Our inspectors will gather evidence as part of the process of conducting a preliminary examination and a decision on whether an investigation will be launched will be taken in the coming days.”