The suspension order was issued on Monday after the footage sparked widespread criticism online.
Police said departmental proceedings have also been initiated against the constable to ascertain whether the use of force complied with established protocols.
The incident reportedly took place during protests linked to the nationwide agitation over the alleged NEET paper leak.
Police had launched a crackdown after demonstrators allegedly blocked roads and clashed with security personnel in parts of Siwan.
Senior police officials said the matter is under investigation and appropriate action will be taken based on the findings of the departmental inquiry.
Authorities have not yet confirmed whether the firing involved live ammunition or was carried out as a warning measure.