Brand was facing an allegation of incitement to violence after making the comment 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.”