Stynes caused outrage last week when she and George Negus mocked Victoria Cross medal recipient Ben Roberts-Smith. Despite a public apology, she has received "severe" social media threats and the show has been dumped by various sponsors.
Melbourne Lord Mayor Robert Doyle, who recently crowned footballer Kewell 'Moomba King of Melbourne', told the Herald Sun that Kewell failed to appear at his scheduled interview to promote the Moomba parade on The Circle because of Stynes's comments.
Doyle claimed: "He pulled out of one [show] because of comments made by the host about our Victoria Cross winner."
He also confirmed that Kewell pulled out of two radio interviews this morning at his football club Melbourne Victory's request.
A Channel Ten spokeswoman confirmed that Kewell was initially due to appear on the show today, but had decided to pull out over the weekend. She did not give any reasons for his decision.
Negus was recently dumped by Telstra from a $25,000 (£17,000) hosting gig for his part in the scandal.
> Channel Ten: 'We have already apologised for war hero jibes'
> George Negus: 'War hero Ben Roberts-Smith not upset about my TV jibes'