Police now say the issue is still under investigation as a "possible bias incident" and not as a hate crime.
According to the cemetery director and a local woman the tombstones fell from age deterioration years ago.
ADL NY regional director Evan Bernstein said that "based on the number of antisemitic incidents amid threats to the Jewish community over the last 6 months or more, it’s natural for people to be on edge. However, I think it is critical that we as a community get all the information first before we jump to any conclusions."
Adding that "we thank the NYPD for all their help and resources."
The cemetery is located in the Mapleton neighborhood, located between Borough Park and Bensonhurst.
The New York Police Department’s hate crimes division has been notified of the incident, the spokesman said, adding that police would investigate on Sunday to see if the incident may have been weather-related.
Local news reports said about five headstones were toppled.
New York Assemblyman Dov Hikind tweeted photos of some of the downed headstones on Saturday night. He said he was alerted to the incident by the Boro Park Shomrim organization, a Jewish security patrol.
In 2010, some 200 headstones were toppled in the same cemetery, also over a Friday night and Saturday, when it is closed.
Washington Cemetery was founded in 1850, and it became a Jewish burial-ground as early as 1857.
The incident brings to four the number of Jewish cemeteries vandalized in the past two weeks, including the Waad Hakolel Cemetery in Rochester, in upstate New York. Dozens of gravestones were toppled and damaged at cemeteries near St. Louis and in Philadelphia as well.
JTA and Reuters contributed to this report.