The accident happened at Grosmont Station on the preserved heritage line on September 21 at 10.30am.
A Class 20 diesel locomotive collided with the rear of a stationary passenger train while travelling at around 10mph.
The RAIB confirmed that five passengers suffered minor injuries and the train sustained damage.
Investigators visited the scene and have determined that as the collision was minor, a safety digest rather than a more in-depth report will be published into the accident and made available to the public within weeks.
A station webcam image of the engine's movements ahead of the impact has also been released.
Following the collision, passengers were removed from the carriages involved and transported back to Whitby.
The incident did mean that several Pullman services were cancelled over the following days, but the railway's annual steam gala went ahead as planned.
The North Yorkshire Moors Railway's head of business development Laura Strangeway said: “I am immensely proud of the team here at the railway - with passenger safety paramount, the situation was managed carefully and as quickly as possible. Whilst there were no serious injuries to passengers, the carriages involved in the incident are now out of operation whilst the investigation is ongoing."