Police are analyzing all CCTV footage from 24 hours before Friday.
According to local councilor Steven Corr, of the Sinn Fein Party, the incident is the latest in a series of vandalism acts at the cemetery.
"These unbelievable attacks on the headstones of dead people needs to stop," he said, according to local news outlet Belfast Live, adding that he felt this was a "deliberate targeting."
“Parents need to impress upon their kids that the cemetery isn’t a playground or a place to gather. Parks, playgrounds and pitches are reopening and this damage and desecration of graves causes untold hurt and distress to all the families who have loved ones buried in the City Cemetery,” he added.
The incident was condemned by other political representatives. One, North Ireland parliamentarian William Humphery, said he was “disgusted and appalled to hear that 10 Jewish headstones have been damaged” and remarked that "this is a very sad day for Belfast," Belfast Live reported.
"Those behind this appalling antisemitic attack are evil," he continued. "A graveyard is a sacred place and should be respected as such. Those responsible are guilty of a most heinous hate crime."
A Belfast City Council spokesman said the council, which operates the cemetery, is working with police and taking steps to "try to address issues of anti-social behavior and vandalism at City Cemetery," according to Irish News.
He added that: "As part of our City Cemetery heritage project, we are planning to create a new visitor center and improve facilities. It is hoped the increased footfall will also help to deter vandalism."