A plane was seen pulling a banner that read "White Lives Matter–Burnley" when it flew over Etihad Stadium before the start of the club's match against Manchester City on Monday.
The aircraft was seen minutes after players and match officials knelt on the field for around 10 seconds to show their solidarity with the Black Lives Matter movement.
Burnley released a statement in response, denouncing the offensive banner.
"Burnley Football Club strongly condemns the actions of those responsible for the aircraft and offensive banner that flew over The Etihad Stadium on Monday evening," the club said.