Matthew P Doyle was arrested on Wednesday after a message was posted on his Twitter profile about confronting a woman in south London.
The 46-year-old from South Croydon was charged on Friday morning with publishing or distributing written material which is threatening, abusive or insulting, likely or intended to stir up racial hatred.
But hours later Scotland Yard said he was "no longer charged". He will not have to attend a planned first appearance at Camberwell Magistrates Court on Saturday morning, Metropolitan Police said.
A police spokesman said: "Matthew Doyle, 46 of South Croydon was charged by police on Friday, March 25, with an offence under Section 19 of the Public Order Act 1986.
"Following discussion with the Crown Prosecution Service (CPS), Mr Doyle is no longer charged with the offence and will not be appearing at court.
"Police may not make charging decisions on offences under Section 19 of the Public Order Act. There will be further consultation with CPS."
Scotland Yard had said he was charged after an investigation by officers at Croydon Police Community Safety Unit.
At least 34 people were killed and more than 200 injured in the terror attacks across Belgium's capital on Tuesday morning.
Prosecutors have confirmed the Brussels bombings, which the so-called Islamic State has claimed responsibility for, were linked to the Paris attacks in November.