A new disciplinary code for pupils, to be voted on next week, calls for "posting libellous or defamatory material... or material containing a (physical) threat" on the internet to be met with sanctions.
These range from calling a meeting with parents - in the case of pupils still in primary school - to possible expulsion for teenagers.
"It would mean anything like, 'Mr Smith is a real you-know-what' or 'I'm going to kick so-and-so's butt after school'," said New York schools spokesman Keith Kalb.
New York's proposals follow similar edicts enacted across America recently to address an increase in the number of students issuing insults and threats and lampooning staff on "social networking" websites such as MySpace.com.
"Schools are struggling to deal with this phenomenon," said Steve Jones, communications professor at the University of Illinois, Chicago.
In May, one Chicago education authority decreed that students would forfeit their right to participate in extra-curricular activities if they were "maintaining or being identified on a blog site which depicts illegal or inappropriate behaviour".
New York's crackdown would not involve staff trawling the internet for offending material. Instead, it would be "complaint-driven", Mr Kalb said.
But Mr Jones warned: "You're going to have people filing all kinds of complaints that they'll have to follow up."
Mr Kalb said online harassment was just as serious as harassment in person.
"We wouldn't let someone do that in the real world, so why let them do it in the cyberworld?"