Thieves took off with a safe containing jewellery amongst other person possessions from Rowley & Sons at Dilston House in Lawrence Street. They also took a projector.
North Yorkshire Police said the burglary happened between 8.30pm on May 18 and 9.45am on May 20.
Martin Rowley, who owns the business, told Yorkpress that the thief almost certainly walked into the building on Thursday afternoon and gone upstairs, with staff believing they were going to offices operated upstairs by another business.
“They probably thought there was cash in the safe but there wasn’t,” he said. “There was jewellery which did not have any great monetary value but was of great sentimental value to the families of five people.
“We have contacted the families and while they are distressed and upset by the theft, they recognise that we are the victims of crime as much as them.”
He said the funeral directors had always operated an ‘open door’ policy, believing that it would not be targeted by criminals in this way in a city like York, but people now had to press a bell to be allowed entry into the building.
Police urged witnesses or anyone with information to get in touch by calling 101, selecting option 2, and asking for Jon Bostwick, emailing email@example.com or passing information anonymously to Crimestoppers on 0800 555 111, quoting reference number 12160087874.