The building was set alight at High Mill Farm, Scalby, at around 5.30pm on Sunday, October 16.
Police are now appealing for witnesses to come forward who may have seen suspicious activity in the area.
A North Yorkshire Police spokesman said: "We are conducting enquiries and are requesting the public’s assistance to help determine the full circumstances surrounding the incident.
"In particular, we are appealing for information about suspicious people that may have been in the area during the time."
Anyone with information that could assist the investigation is asked to contact 101, select option 2, and ask for Liam Cromack.