West Yorkshire Police have now had to remove the floral tribute from the memorial on Kirkgate, near Leeds Minster, close to the spot where Sergeant John Speed was shot dead in 1984.
The 39-year-old was fired on at point-blank range by a well-known local criminal called David Griceworth when he went to a colleague's aid.
The memorial has also been desecrated in the past, most recently in 2010, when silver paint and swastikas were daubed on the stone and flowers ripped up.
Chief Superintendent Steve Cotter said:
“Sergeant John Speed was murdered in the line of duty and each year we continue the important tradition of remembering our fallen colleague.
“I was at the wreath-laying ceremony at his memorial stone in Kirkgate on Sunday with colleagues, and I’ve been made aware today that the wreath we laid has been damaged. We have removed it now because of that.
“We are looking into what has happened and if someone has done that as a deliberate act of vandalism and disrespect then I and my colleagues in West Yorkshire Police and the wider policing family are truly appalled.
“If anyone witnessed anything at the scene or has any information that could assist us in identifying the person responsible then we would ask them to contact us.”
Sgt Speed was shot after going to the aid of a colleague who was fired on during a routine check on two men acting suspiciously near Leeds Parish Church.
PC John Thorpe, 33, who was first at the scene, had spoken only a few words when one of the men pulled out a handgun and opened fire. Gricewith, a garage owner, was only identified as the gunman after his own death two years later.
Gricewith might still have been alive and free today if he had been able to resist the urge to carry out an armed robbery. When a police chase followed a raid on a supermarket at Stockton-on-Tees, Cleveland, more than two years after Sgt Speed's murder, Gricewith's sawn-off shotgun went off accidentally, shooting him in the stomach, when police rammed his van. He died soon afterwards. Information obtained from a girlfriend after his death helped to confirm growing police suspicions that Gricewith was the killer.