The ten graves in the Jewish cemetery on the Falls Road in West Belfast, Ireland were damaged on Thursday evening are being investigated as a hate crime.
PSNI Insp Róisín Brown said she was "appalled" at the incident, which happened "where members of the community come to pay their respects".
"The damage to these graves shows a total lack of respect for others and will have a significant impact on individuals and families within the Jewish community," she said.
Insp Brown encouraged the local community in west Belfast to hold those responsible to account for their actions and contact police with information.
Some of the graves date back to the 1870s and are in a walled-off section of the cemetery, which is often locked.
The cemetery is maintained by Belfast City Council. Sinn Féin councillor Steven Corr attended the graveyard on Friday to help with the clean up. Writing on social media, he said "these attacks on the headstones of dead people need to stop".
North Belfast DUP MLA William Humphrey said he was "disgusted and appalled" to hear about the attack. "This is a very sad day for Belfast," he said. "I have nothing but the highest regard for the Belfast Jewish community, which continues to have my full support."
Mr. Humphrey added those responsible were "evil" and and were guilty of "a most heinous hate crime".