Matthew Doyle, 46, of south Croydon, was charged on Friday morning under Section 19 of the Public Order Act.
Following discussions with the Crown Prosecution Service (CPS), the Met said he was "no longer charged" and will not be appearing in court.
It said police may not make charging decisions over section 19 of the Act.
Mr Doyle, who was arrested on Wednesday, had been charged with publishing or distributing threatening, abusive or insulting material, likely or intended to stir up racial hatred.
It followed the posting of a message on his Twitter profile about confronting a Muslim woman in south London over the Brussels attacks, which was widely shared on social media and spawned a wave of parodies.
The Met said further consultation with the CPS would take place.
Police have dropped a race-hate charge against a man who allegedly tweeted about confronting a Muslim woman over the Brussels terror attacks.