The raid happened at about 11.30pm on Saturday, when the offender broke into Yay Coffee, in York Place.
Police said they smashed a window at the front of the premises before climbing into the shop.
They then searched the shop, stole the cash till and fled from the scene.
A North Yorkshire Police spokeswoman said: "We are requesting the public’s assistance to help establish the full circumstances surrounding the incident. This was a busy Saturday night and it is believed that members of the public may have seen the offender.
"In particular, we are appealing for information about the offender and any witnesses who saw the burglary."
Anyone with information is asked to call police on 101, quoting reference number NYP-19052018-0645.