Police have, however, warned that such pranks could go horribly wrong in a country where people are constantly on edge for fear...
"Police operations are continuing in different areas to protect public places and prevent further incidents," police spokesman Micky Rosenfeld told AFP.
He said that about 12 youngsters, including two 14-year-olds, were arrested over the past few days.
A previous police statement said that "dozens of youngsters from all parts of the country were detained for questioning after putting masks on their faces in order to sow fear and panic among the public."
Rosenfeld said that they sought only to frighten people, not to harm them.
"There haven't been any attacks. It's just been people dressed up and walking around with fake axes, fake knives, etcetera," he said.
Police have, however, warned that such pranks could go horribly wrong in a country where people are constantly on edge for fear of militant attacks and where many carry firearms.
"There is a concern that such pranks will be interpreted as a real threat and will cause harm to the youngsters," said a statement last week.
"It is absolutely forbidden for people to take the law into their own hands and harm wearers of masks."
Local media said that a victim of an incident in the southern city of Beersheba last week stabbed his tormenter, causing moderate injuries.
Police did not confirm the reports.
Media have suggested a link between the phenomenon, which appears to have broken out around the beginning of October, and the September 14 release in Israel of the film of Stephen King's "It," featuring an evil clown who preys on teenagers.
The plague of scary clowns broke out in the United States last year.
There were sightings in South Carolina of people dressed as clowns trying to lure children into the woods.
The appearances soon spread, with more than 20 states reporting incidents, and although most were pranks or unverified threats, police made a handful of arrests, including for physical attacks.
The craze, fanned through social media, spread to Canada, Europe, South America and Australia.
The Israeli police advised members of the public confronted by a masked person not to engage with them.
"In these situations, move away from the scene and report it to the police as soon as possible," the official police Facebook page says.