The Prime Minister's official spokesman said: "The Prime Minister has been repeatedly clear that politicians should be able to go about their work and campaign without harassment, intimidation or abuse.
The comment made by Jo Brand is being assessed by the Metropolitan Police following an allegation of incitement to violence, the force said
"I note that Brendan Cox has said that violence and intimidation should not be normalised and we should consistently stand against it. The Prime Minister shares this view. It is for the BBC to explain why it considers this to have been appropriate content for broadcast."
Brand, 61, appeared on Victoria Coren Mitchell's Heresy on Tuesday night when in reply to a question about the state of UK politics she said: "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, who was last month covered in milkshake during a campaign walkabout in Newcastle city centre, accused Brand of inciting violence.
He tweeted on Wednesday: "This is incitement of violence and the police need to act."
Broadcasting watchdog Ofcom has said the episode of BBC Radio 4's Heresy in which Jo Brand made her "battery acid" joke has now received 65 complaints.
The Metropolitan Police said in a statement: "Police have received an allegation of incitement to violence that was reported to the MPS on 13 June.
"The allegation relates to comments made on a radio programme. The allegation is currently being assessed.
"There have been no arrests and inquiries are ongoing."