Brand was facing an allegation of incitement to violence following the remark on BBC Radio 4 show Heresy.
The comedian, 61, later admitted the joke was “crass and ill-judged” but reportedly said she did not feel she had made a “mistake”.
In a statement, Scotland Yard said: “Police received an allegation of incitement to violence on 13 June, relating to comments made on a radio programme.
“The referral has been considered by the MPS and no further police action will be taken in relation to this allegation.”
Brand made the joke while speaking about the recent trend of throwing milkshakes at right-wing politicians.
When asked by another panellist about the state of UK politics, she replied: “Well, yes I would say that but that’s because certain unpleasant characters are being thrown to the fore and they’re very, very easy to hate and I’m kind of thinking: ‘Why bother with a milkshake when you could get some battery acid?’
“That’s just me. I’m not going to do it, it’s purely a fantasy, but I think milkshakes are pathetic, I honestly do, sorry.”
Brexit Party leader Nigel Farage publicly criticised the comment, saying it was an “incitement of violence and police need to act”.
The right-wing politician was covered in milkshake while on a campaign walkabout in Newcastle last month.
Commenting again on Twitter, he said: “I am sick to death of overpaid, left-wing, so-called comedians on the BBC who think their view is morally superior.
“Can you imagine the reaction if I had said the same thing as Jo Brand?”
According to the Press Association, the allegation reported to police was not made by Mr Farage or the Brexit Party.
The BBC has said it will edit the programme after 65 complaints were received by Ofcom.
In a statement, it said the comments were not intended to “encourage or condone violence”.
“Heresy is a long-running comedy programme where, as the title implies and as our listeners know, panellists often say things which are deliberately provocative and go against societal norms but are not intended to be taken seriously,” it said.
“We carefully considered the programme before broadcast.
“It was never intended to encourage or condone violence, and it does not do so, but we have noted the strong reaction to it.
“Comedy will always push boundaries and will continue to do so, but on this occasion we have decided to edit the programme. We regret any offence we have caused.”
Comedian David Baddiel, who created Heresy, said the BBC appeared “cowardly” for censoring Brand’s joke on the show.
“If it was up to me, I would have kept that line in for the repeat,” he told Newsnight.
“Apart from anything, it’s a bit silly when it’s had massive coverage to cut it out – that looks a bit cowardly.”
After making a scheduled appearance at the Henley Literary Festival in Oxfordshire, Brand sidestepped questions from Sky News about the incident.
She did comment that freedom of speech in comedy was “extremely important”.