Gwent police had been looking into complaints about the Brexit party leader's speech to an audience of around 500 supporters in Wales.
In a tweet, Alliance party MEP Naomi Long, asked police on Twitter if they would be investigating “this clear case of incitement to violence against staff in the civil service”.
Police said the comments did not constitute a criminal offence.
His remark came amid increased concern over the language being used by some politicians over Brexit.
The Brexit Party leader allegedly criticised civil servants at a rally in Newport, South Wales.
Gwent Police tweeted: "Thank you for your message. We have been made aware of comments made last night in Newport and we are looking into these allegations."
Referring to the comments, Nigel Farage tweeted: "I should have said ‘take the axe’, which is a more traditional term for cuts."
At the event, Farage also described John Bercow as a “ghastly little man” and referred to Xavier Bettel as “that perfectly vile little pipsqueak of a prime minister in Luxembourg”.
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Boris Johnson came under intense criticism after briefing his cabinet on preparations for a populist election campaign that will accuse his opponents of “surrender” to the EU.
In the Commons on Wednesday, he told told the Labour MP Paula Sherriff, who disclosed she received death threats every day, that her concerns about aggressive language fuelling violence were “humbug” and another that the best way to honour the murdered Labour MP Jo Cox was to “get Brexit done”.
The Prime Minister spoke at a meeting of the 1922 Committee of Conservative MPs the morning after being branded a disgrace for dismissing concerns about his inflammatory language in light of Cox’s murder by a far-right extremist.
The Prime Minister’s remark on Wednesday came after several MPs drew upon the memory of Mrs Cox when urging him to curb his “violent” and “dangerous” language.
Mrs Cox, 41, was a staunch Remain supporter when she was murdered just days before the Brexit referendum.