The complaint was made last Friday in relation to comments made by guest panellist Camilla Long. The party claims her suggestions could hamper Farage's chances of winning the South Thanet constituency.
On the show, Long claimed: "I went [to South Thanet] more than Nigel Farage. By the time I arrived there he’d only been a few times."
Ukip argues the comments are false and are in breach of section 106 of the Representation of the People Act and could influence the result.
It added that Long has in the past made disparaging comments about the South Thanet constituency and Farage's chances of victory.
A journalist at the Times and Sunday Times, Long penned an article in March calling the Isle of Thanet an "erupted spleen" at the eastern edge of England that, "given enough anger, enough bile, enough precision dyspepsia, could suddenly, magnificently, detach itself entirely this election".
A Ukip spokesman told City A.M.: "Camilla Long made false statements about a candidate at this election. The BBC chose to air it. If this isn't a breach of Section 106 of the Representation of People Act, then we don't know what is. "
However, Kent police told ITV News "the matter has been reviewed by officers but there’s no evidence of any offences and there will be no further action".
The BBC has refused to back down over the show with spokesperson commenting:
Britain has a proud tradition of satire, and everyone knows that the contributors on Have I Got News for You regularly make jokes at the expense of politicians of all parties.
The latest batch of constituency polls from Lord Ashcroft show Farage two points behind his Tory opponent Craig Mackinlay on 32 per cent.