On Friday's show, journalist Camilla Long made claims about how often Mr Farage had visited Thanet South, where he is standing for election.
UKIP said that broke a law that bans false statements about candidates.
The BBC said the show often made jokes at the expense of politicians. Kent Police said it would not take action.
Camilla Long had visited the constituency for an article published in the Sunday Times last month.
UKIP advisor Raheem Kassam said: "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."
The law says it is illegal to make a "false statement of fact in relation to the candidate's personal character or conduct" before or during an election.
However, Kent Police said: "It was suggested that the comments breached the Representation of the People Act.
"The matter has been reviewed by officers but there's no evidence of any offences and there will be no further action."
A BBC statement said Britain had "a proud tradition of satire".
It added: "Everyone knows that the contributors on Have I Got News for You regularly make jokes at the expense of politicians of all parties."
UKIP has also reportedly complained to the Metropolitan Police, although a spokesperson for that force said she had no information about such a complaint.
The full list of candidates standing for election in Thanet South can be found here.
UKIP has complained to the police over comments about leader Nigel Farage on an episode of BBC One's topical quiz Have I Got News For You.