The attack happened on Saturday and has sent shock waves through the community.
The cemetery at Old Hall Lane was vandalised on Saturday, with damage caused to three separate chapels, a prominent headstone and windows and sinks.
CCTV was also stolen from within one of the chapels.
A full investigation has been launched and enquiries are ongoing.
Now local leaders have issued a joint statement condemning what happened.
Councillor Tamoor Tariq, Bury Council’s cabinet member for communities and safer neighbourhoods, said: “I condemn in the strongest possible terms the abhorrent act of violence that took place over the weekend at the cemetery in Philips Park. An attack on one part of our community is an attack on all our community and we will work together to get to the bottom of this.
“I want to pay tribute to Greater Manchester Police who have moved very swiftly to investigate this matter as a hate crime, and I would urge anyone with any information to come forward at the earliest opportunity. We cannot allow the actions of some to deter us from our work in rooting out intolerance, prejudice and hatred in all its forms.
“I am chairing a meeting today with representatives of the council, the Jewish community and the police to discuss ways to best offer support to the Jewish community at this time.”
Council leader Rishi Shori added: “This was a deliberate act of desecration in a Jewish cemetery, clearly a crime driven by hatred. The people of Bury will be horrified and dismayed by this destruction, which is not a true reflection of our borough. We will now redouble our efforts in tackling hatred and building strong and safe communities.
“The timing of this incident is all the more poignant, coming after Holocaust Memorial Day and Hate Crime Awareness Week, both times when our communities stood side by side in solidarity and friendship.
“The council is working with the police and the broader community to provide reassurance. I am hoping the perpetrators of this senseless crime can be found quickly. “
Marc Levy, North West External Affairs Manager for the Jewish Leadership Council, said: “The targeting and desecration of a Jewish cemetery in Whitefield has understandably caused deep distress to the local Jewish community. The police are rightly treating this appalling act of vandalism as a hate crime.
“I would like to place on record my thanks to everyone at Bury Council and Greater Manchester Police for the exemplary way in which they have dealt with this sensitive and difficult situation.”
And Sharon Bannister, President of the Jewish Representative Council (Greater Manchester & Region), said: “The local Jewish community is once again deeply distressed by yet another senseless desecration of a Jewish cemetery.
"On this occasion the grave targeted was that of a leading Rabbi and this will cause additional pain within the orthodox Jewish community whose members would visit the grave in order to seek inspiration and guidance. We also appreciate the support and swift response from both Bury Council and Greater Manchester Police.”