PC Gillian Weatherley was dismissed for "gross misconduct", Scotland Yard said.
She was sacked for leaking information about the 2012 argument between police officers and MP Andrew Mitchell.
PCs Keith Wallis and James Glanville have already been sacked for gross misconduct, with two more officers yet to face such hearings.
Mr Mitchell was accused of calling officers plebs during the argument at the gates of Downing Street - an allegation he has denied.
The Conservative MP resigned as chief whip in the wake of the controversy.
A panel chaired by Commander Julian Bennett found PC Weatherley had breached professional standards in relation to "honesty and integrity; orders and instructions; confidentiality; discreditable conduct and challenging and reporting improper conduct".
The Met said it had brought the gross misconduct case after the Crown Prosecution Service decided in November that criminal prosecution was not appropriate.
PC Weatherley was on duty at the Downing Street gates on the night of the dispute, 19 September 2012, and the Met said she had exchanged several messages with PC Glanville over the next three days.
It added that she had subsequently given "inaccurate and misleading statements" to detectives from Operation Alice - the investigation into alleged misconduct by officers.
Scotland Yard said it "would not disclose" how information was leaked to the press by PC Weatherley or to whom.
A police officer has been sacked over press leaks about the "plebgate" affair, becoming the third Met PC to be dismissed over the row.