It comes amid an ongoing row in the Commons about MPs’ choice of words after Boris Johnson dismissed the dangers of inflammatory language as “humbug”.
Alliance Party MEP Naomi Long said Farage’s comments amounted to “a clear incitement to violence” against civil service staff.
But on Saturday evening, Gwent Police said it would not be taking any further action over the speech.
Assistant chief constable Rhiannon Kirk said the force had received a number of “comments and concerns” after a clip from a speech Farage made at The Neon in Newport on September 21 was shared on social media.
“We are aware of the heightened tensions that exist regarding use of language, and take all allegations and concerns from members of the public very seriously,” she said.
“However, following a thorough assessment, it is our view that the comments in the video, do not constitute a criminal offence. As such, Gwent Police will not be taking any further action.”