The 14-year-old boy was charged under the Communications Act 2003 after staff found abusive comments and pictures on an online page.
Another 14-year-old boy was also charged last month.
The Facebook page, targeting teachers at schools in Clackmannanshire, has been deleted.
A headteacher urged parents to check their children's mobile phones and laptops for any involvement and said the page was "designed to deliberately cause humiliation, defamation and insult to staff".
Clackmannanshire Council said staff had been working with parents, staff and police to resolve the matter.
Alan McKenzie, acting general-secretary of the Scottish Secondary Teachers Association, said: "This is yet again another example of kids being over-technologised."