The club say images were circulated online showing its supporters mocking Bradley, who died in 2016.
Sheffield Wednesday were beaten by Sunderland 3-0 at the game on Friday.
Bradley was a Sunderland fan, who was diagnosed with neuroblastoma - a rare type of cancer - when he was 18 months old.Well-wishers raised more than £700,000 in 2016 to pay for him to be given antibody treatment in New York, but medics then found his cancer had grown and his family was informed his illness was terminal.
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