The comedian made the joke in June, after several political figures had milkshake thrown on them.
During an appearance on Radio 4’s Heresy show, she said: “I’m thinking why bother with a milkshake when you could get some battery acid.”
After making the remark, Brand added: “I’m not going to do it, it’s purely a fantasy. But I think milkshakes are pathetic.”
Ofcom said it received 65 complaints about the episode.
Following the broadcast, Brexit Party leader Nigel Farage, who just days earlier had had a milkshake thrown at him while campaigning in Newcastle, accused Brand of “inciting violence”.
Commenting 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.”
The corporation’s Executive Complaints Unit (ECU) has since said it did not uphold the aspect of complaints on incitement of violence.
Its reasoning was it had “considered the context in which the words were spoken”.
A spokesperson from the BBC said: “We note the findings and that the BBC’s ECU concluded the comments did not condone violence and that no subject matter should be beyond the scope of comedy.”
At the time, Scotland Yard said a referral was considered, though no further police action would be taken in relation to the allegation.
It was believed the allegation reported to police was not made by Mr Farage or the Brexit Party.
The comedian apologised for the joke, calling it “crass and ill-judged”.
The BBC removed the comment from its catch-up show.