Hoax bomb threats were also made to at least 33 schools around the country in February last year.
The calls happened over two days and the police believed they were linked.
National manager of criminal investigations, Detective Superintendent Tim Anderson said the threats caused considerable disruption and fear.
"I hope that today's development will bring some comfort to the victims involved in New Zealand.
"This was a relatively sophisticated attack which utilised voice over internet telephone calls."
Anderson said the arrest showed the value of the strong international partnerships New Zealand Police have with overseas law enforcement jurisdictions.
"I am mindful that we must let the Israeli judicial process run its course, meaning that we are limited in the information we can provide."
Israeli police spokesman Micky Rosenfeld said the teenager, from the south of Israel, holds Israeli and US citizenship.
Rosenfeld said on Thursday that the suspect used technology to make himself harder to track and mask his identity while making the threats, which caused "fear and panic in Jewish communities" around the world.
He added that, in one instance, bomb threats made by the suspect caused a plane to make an emergency landing.
Since the beginning of 2017, Jewish centres in some 20 US states have reported receiving more than 100 hoax bomb threats, according to US media outlets.
The increase in bomb threats, and in vandalising of several Jewish cemeteries, have prompted talk of a rise in anti-Semitism in the US, with a leading US Jewish group, the Anti-Defamation League (ADL), issuing a nationwide "security advisory" last month.
The ADL said today that it was "relieved and thankful" that law enforcement had made the arrest.
"While motivation is unclear, the impact is crystal clear," the group said on Twitter.
"Calling in bomb threats to Jewish institutions is an anti-Semitic act."
An Israeli court ruled later on Thursday that police could keep the teenager, whose name cannot be disclosed, in detention until April 30.