Future Sound Asia says Healy's actions, including a same-sex kiss from the stage, left it in financial ruin after the Malaysian canceled the event over his statements.
The duo first sparked romance rumors in early May.
Since the news about her split from Joe Alwyn last month, rumors of a new Taylor Swift romance have already been swirling.
The intimate moment took place at the end of "Robbers," a fan favorite track.
A shirtless Healy devoured the meat before crawling across the stage.
