The FIR has been registered in Bijnor.
The Congress, SP and BSP have launched a joint attack on Narendra Modi's close aide Shah and Congress even want him to get "arrested".
However, the BJP has said that there is nothing wrong in Shah's remarks.
BJP President Rajnath Singh along with other party leaders claimed that there were "nothing wrong" in Shah's statement.
On Sunday, Election authorities in Uttar Pradesh sent the CD of the controversial remarks by Amit Shah along with the report of District Election Officer to the Election Commission.
Sources said the Chief Electoral Officer of UP had yesterday taken cognisance of Shah's statement and had sought the CD along with a detailed report from the district authorities.
These have been sent to the Nirvachan Sadan-- the headquarters of the Election Commission here, they said.
The BJP leader has sparked a row with his comment that the general election, especially in Shamli village in Muzaffarnagar district, western UP.
He had said, "this election is about voting out the government that protects and gives compensation to those who killed Jats. It is about badla (revenge) and protecting izzat (honour)".
Congress has demanded the arrest of Shah for his remarks while BJP has said that he had talked of taking revenge from Congress and his statement was not against any particular community.
"Shah's rank communal remark shows that BJP does not understand the idea of India and its agenda is to divide communities and get votes. That it the only agenda of this communal party of India," Congress party spokesperson Abhishek Singhvi told reporters.
Union Minister Beni Prasad Verma also alleged SP and BJP were hand in glove with each other in communalising elections and sought a "ban" by the Election Commission on campaigning by leaders Narendra Modi and Amit Shah in Uttar Pradesh.
The CPI-M also urged the Election Commission to bar BJP leader Amit Shah from addressing election meetings after providing evidence of his "hate speeches" in Uttar Pradesh.