The distinctive gravestone was a tribute to a renowned steeplejack family. It was erected in 1895 when Sarah Kidney, the wife of Thomas Kidney, died.
Thomas was a well known chimney-feller and steeplejack. The family held gold and silver medals for his work.
He was laid to rest in the family plot in 1914, when he died aged 82 and was hailed the "oldest steeplejack in England."
By 1924 the firm had demolished a total of 180 chimneys, making a world record.
The theft of the chimney was discovered days ago, when the graveyard was being cleared by Leeds Parks Department and John Smeaton High School pupils to prepare for spooky guided tours marking the launch of a Beckett Street Cemetery guidebook called Surprising Lives.
Now local historians say the loss could be a blow for the city's social history. The Friends of Beckett Street Cemetery have launched their own investigation and police are appealing for any information.
Local historian Penny Wainwright, who is co-author of the new guidebook on the cemetery and trustee of the Thackray Medical Museum, said: "It is a very unusual memorial in the shape of an industrial chimney.
"Somebody has stolen the memorial and when we reported it to police they said it was probably stolen to order.
Thrilled
"If there are any living relatives of Thomas Kidney then I hope they get in touch."
In a report in the Yorkshire Evening Post in 1926 the family also claimed the title of having the youngest-ever steeplejack.
Mr Kidney's great grandson, Tommy, had thrilled a crowd at Scarborough at the age of five by climbing 120 ft up the steeple of Albemarle Church, where he stood for half an hour on a plank erected around the weathercock.
The reports states: "He returned to earth as calmly as he had left it."
Anyone who can help or any relatives of Thomas Kidney should contact Alison Bellamy at the YEP on 0113 243-2701, ext 1277.

alison.bellamy@ypn.co.uk