The 23-year-old England player led fans in three chants which mocked rivals Tottenham. He later apologised.
Wilshere was found guilty by the FA of making and/or inciting comments which brought the game into disrepute.
He had a similar outburst last year, and has been "severely warned" by the FA about his future conduct.
Wilshere admitted a misconduct charge after taking to the microphone during the parade last month.
He was spoken to by Arsenal staff after this latest incident but the club said they would not be taking action.
The Gunners secured a record-breaking 12th FA Cup win by beating Aston Villa 4-0 at Wembley on 30 May.
Arsenal midfielder Jack Wilshere has been fined £40,000 after singing offensive songs during the club's FA Cup victory parade in London.