The 23-year-old took to the microphone in front of thousands of fans outside the club's Emirates Stadium, mocking Premier League rivals Tottenham.
Wilshere sang two anti-Spurs songs on a balcony alongside his team-mates.
He launched a similar attack during last year's victory celebrations. The club is yet to comment.
The appearance marked the end of the club's victory parade.
Supporters at the ground braved the rain for hours to celebrate the team's record-breaking 12 FA Cup win.
Players had travelled to a civic reception at Islington Town Hall in an open top bus at 11:00 BST.
Wilshere came on as a second-half substitute during Saturday's final, which saw the Gunners thrash Aston Villa 4-0.
The win makes Arsenal the most successful club in FA Cup history.
Arsenal midfielder Jack Wilshere has led fans in an expletive-laden chant during the club's FA Cup victory celebrations.