Choudhary, a civil engineer and chairman of Dev Public School in Agra, was booked and arrested Monday under section 153A of the Indian Penal Code and 66A/67 of IT Act for "defamatory and inflammatory posts against a particular community", police said.
His laptop, SIM card and data card were also seized.
Police acted after some Facebook users complained against the posts.
However, Choudhary's lawyer said the Facebook account was hacked and someone else posted the material.
There were reports that Choudhary was held for defamatory posts against politicians. But a police source said he was arrested allegedly for the communal hatred he was inciting.