The fire began in the thatched roof of the 14th-century building and destroyed the middle section, though fire crews managed to save the ground floor.
Police were invited to the scene on Thursday after North Yorkshire Fire and Rescue Service investigators became suspicious and requested their involvement.
A police statement read: "We’re investigating the serious fire at a restaurant in Harome, and appealing for witnesses and information about the incident.
"Emergency services were called to the fire at The Star Inn, Harome, just before 10.15pm on Wednesday night. Following an examination of the scene by police crime scene investigators and fire investigation officers, it’s now believed that the fire was started deliberately.
"A number of groups of people were in the area around the time of the fire, and we’re urging anyone with information about the incident to contact us. Please call North Yorkshire Police on 101, quoting reference 12210248468, or email [email protected]"
The Star's owner, Michelin-starred chef Andrew Pern, has already told The Yorkshire Post that it will take around a year to rebuild the gastropub due to a shortage of specialist thatchers and materials.
He has redeployed staff to work at his other restaurants in York and Whitby.
Staff also managed to retrieve rare and valuable Mouseman furniture from the restaurant.