A newspaper columnist has said she was "incredibly upset" by a Twitter message allegedly calling for her to be stoned to death.
Tory councillor Gareth Compton was arrested over the posting on his private account on the micro-blogging site, police said.
He was questioned and released on bail following his arrest, which was followed by suspension from the Conservative Party.
The post on Mr Compton's profile, which has since been removed, reportedly read: "Can someone please stone Yasmin Alibhai-Brown to death? I shan't tell Amnesty if you don't. It would be a blessing, really."
In a message posted on the site, Mr Compton, councillor for Erdington, Birmingham, apologised: "I did not 'call' for the stoning of anybody. I made an ill-conceived attempt at humour in response to Yasmin Alibhai-Brown saying on Radio 5 Live... that no politician had the right to comment on human rights abuses, even the stoning of women in Iran. I apologise for any offence caused. It was wholly unintentional."
Ms Alibhai-Brown told the BBC a friend alerted her to the message, which she did not regard as an example of comedy. "I was just incredibly upset," she said. "He was specifically asking that I should be stoned because he didn't agree with a view I expressed. This is not debate, it's incitement."
Describing the era of internet blogging as a "challenge", she said: "There is this whole unreal virtual world where people think they can tweet or blog anything they want about anybody and there is no accountability. And it spreads so quickly."
A member of the public reported it to the police, she added.
A spokeswoman for West Midlands Police said: "We can confirm a 38-year-old man from Harborne, Birmingham, has been arrested for an offence under section 127 (1a) of the Communications Act of 2003 on suspicion of sending an offensive or indecent message. He has been bailed pending further inquiries."
Steve McCabe, Labour MP for Birmingham Selly Oak, said: "It is staggering that the Conservative Party allowed Gareth Compton to represent the people of Birmingham in the first place. He said: "His despicable comments on Twitter show that he has no place in public office. This sorry saga calls into question the leadership of the Conservative Party at all levels, they must stop dithering and force him to resign his seat on Birmingham City Council."