No arrest had so far been made in this connection, but three people were detained for questioning, he added.
Mahendrabhai Sodha and Ranjitbhai Sodha, the sons of Anand MLA Kantibhai Sodha Parmar, were charged after they were purportedly seen in the video firing several rounds in the air from their guns, along with other unidentified persons, Anand Town police station inspector NK Chauhan said.
The incident came to light after the video started circulating on the social media, he added.
"We have registered an FIR against the Sodha brothers and six others, along with some unidentified persons, based on the video, wherein they are seen firing in the air," he said.
The police were trying to identify the others, who were also seen firing in the air, Mr Chauhan said, adding that the FIR was registered under sections of the Indian Penal Code and relevant provisions of the Arms Act.
The video was apparently shot three days ago, when the Kshatriya Samaj, an organisation of the Kshatriya community, had organised "Dayro" -- a traditional music performance -- to mark the second anniversary of its foundation.
"We have detained three persons and an investigation in the matter is on," he said, adding that no arrest had so far been made.