Turkish Interior Minister Süleyman Soylu has described the incident as a "heinous attack".
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Five teenagers have been arrested on suspicion of vandalising dozens of graces at Turkey's largest Jewish cemetery.
A total of 81 tombstones were "destroyed" on Thursday night, according to the governor of Istanbul. Community leaders had initially said that 36 graves had been damaged "around midnight".
Images on social media show several tombstones toppled over and smashed on the floor of the cemetery.
The teenage suspects -- all aged between 11 and 13 -- were detained and an investigation is ongoing.
Turkish Interior Minister Süleyman Soylu immediately condemned the "heinous attack on Hasköy cemetery".
"Those who try to disrupt our unity and solidarity with such provocative attacks will never be allowed," he added on Twitter.
The area around the Hasköy Jewish cemetery in Istanbul is home to the vast majority of Turkey's 15,000 Jews.