Police are appealing for information after a number of graves were damaged in Harehills Cemetery.
The incidents are believed to have taken place towards the end of last week, possibly overnight between Thursday 18 and Friday 19 March.
In total 18 graves have been vandalised; all of which are in an area of the cemetery predominantly used by Muslim families.
One headstone has been broken and a number of name plaques on wooden stands have been damaged or ripped off.
Inspector Nik Adams, who leads the Gipton and Harehills Neighbourhood Policing Team, said: "This incident has caused a great deal of upset and distress to a number of people in the local community and a joint investigation has been launched by North East Leeds CID and the Gipton and Harehills Neighbourhood Policing Team.
"Over the weekend we have worked alongside community and religious leaders to identify and contact the next of kin of those whose graves have been affected by this mindless act of vandalism.
"We have also undertaken a full forensic examination of the scene which has proved encouraging and we are currently awaiting the results of that.
"At this stage in the investigation we are keeping an open mind on whether the graves were deliberately targeted because they were linked to Muslim families or whether they were vandalised because of their proximity to a nearby path and two thoroughfares that run through the cemetery.
"We are determined to catch those responsible and I would ask that anybody who was in the area of the cemetery on Thursday evening and witnessed anything suspicious to contact us.
"This incident undermines much of the work both ourselves and Leeds City Council have undertaken during the last year to improve security at the cemetery with increased patrols by neighbourhood wardens and police officers.
"I would like to reassure local people that everything is being done to find those responsible and bring them to justice."
Anyone with information is asked to contact Stainbeck CID via: 0845 60 60 606 or call Crimestoppers anonymously and in confidence on: 0800 555 111.