A plane carrying a banner declaring 'White Lives Matter Burnley' flew over Manchester City's Etihad Stadium on Monday at the start of the Premier League game against Burnley.
The plane appeared shortly after players from both teams took a knee in support of the Black Lives Matter movement. There was no indication who had organised the plane and banner.
Burnley issued a statement at halftime saying the Lancashire club "strongly condemns" the actions and adding that they will work with authorities to identify those behind the move and issue lifetime bans.
All of the players in the 12 Premier League games since the restart of the season after the Covid-19 stoppage have worn 'Black Lives Matter' on their shirts in place of their names.
This follows the league formally joining the international protest campaign sparked by the death last month of George Floyd, a Black man, while in Minneapolis police custody.
Burnley said: "The club has a proud record of working with all genders, religions and faiths through its award-winning Community scheme, and stands against racism of any kind.
"We are fully behind the Premier League's Black Lives Matter initiative and, in line with all other Premier League games undertaken since Project Restart, our players and football staff willingly took the knee at kick-off at Manchester City.
"We apologise unreservedly to the Premier League, to Manchester City and to all those helping to promote Black Lives Matter," the club said.
Burnley captain Ben Mee said after the game, which his side lost 5-0, that the players had heard "whispers" that something may have been planned and that he was embarrassed by the scene.
"I am ashamed and embarrassed that a small number of our fans have decided to fly that around the stadium. It is not what we are about. They have missed what we are trying to achieve," said Mee, who began his career with City.
"These people need to come into the 21st century and educate themselves. They don't represent what we are about, the club is about, the players are about and the majority of fans are about.
"I've heard it is a small number that have arranged this and I hope it doesn't happen again. I don't want to associate it with my club. I don't want to see this in the game.
"It is not right. We totally condemn it. These people can learn and be taught what Black Lives Matter is trying to achieve."