The explosion early on Saturday at the school in an upscale residential neighbourhood on the south side of Amsterdam damaged a rain pipe and charred an outer wall, and caused no injuries.
Mayor Femke Halsema said the incident was taken very seriously, and would lead to increased security at Jewish institutions.
"This is a cowardly act of aggression against the Jewish community," Halsema said.
"Jewish people in Amsterdam are increasingly confronted with anti-Semitism. This is unacceptable."
The school is the only one specifically for orthodox Jews in the Netherlands, and is largely fenced off by a pointed, metal outer wall due to earlier threats.
Security at synagogues and Jewish institutions in the Dutch capital had already been heightened after an overnight arson attack at a synagogue in the centre of Rotterdam on Friday.
In neighbouring Belgium, an explosion caused a fire at a synagogue in Liege on Monday.
Dutch Prime Minister Rob Jetten called the attack in Amsterdam "horrible" and said it understandably caused "fear and anger" in the Jewish community.
"The safety of Jewish institutions has our full attention," he said in a post on X.
Concerns about possible attacks against Jewish communities around the world have risen following US and Israeli attacks on Iran and a subsequent response from Tehran.
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