The FIR was registered against Hindu Yuva Vahini vice-president Aditya Pandit at the Civil Lines police station on a complaint by a group of students from the Aligarh Muslim University.
The AMU students, including former vice-president of the AMU Students' Union Nadeem Ansari, had on Thursday met senior district police officials demanding that the National Security Act be invoked against Pandit.
They also demanded his immediate arrest.
The offensive post has been removed from Pandit's Facebook wall.