The SFC Chicken shop, on North Marine Road, was targeted between 10.45pm on August 25 and 11am on August 26.
Police today have appealed for information, and say they believe the damage was caused by a large brick.
A large glass window and glass door at the front of the takeaway were smashed.
A North Yorkshire Police spokesperson 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 anybody seen committing the damage or being in that area."
Anyone with information is asked to contact police on 101, quoting reference number 12170152172.