Police say Birmingham city councilor Gareth Compton was arrested on suspicion of sending an offensive or indecent message. He was released on bail pending further inquiries.
Media reports say the post on the microblogging site said "Can someone please stone Yasmin Alibhai-Brown to death? I shan't tell Amnesty if you don't. It would be a blessing, really."
The post appears to have been removed. On Thursday Compson tweeted an apology for his "ill-conceived attempt at humor."
Alibhai-Brown is a liberal columnist for The Independent newspaper.
The Conservative Party said Compton had been suspended indefinitely.
