The band – behind hits such as “Robbers” and “It’s Not Living” – are currently on tour.
During one performance, video of which has circulated online, Healy, 33, appeared to perform a Nazi salute while marching on the spot.
He made the action during a performance of The 1975’s song “Love it If We Made It”, as he sang the lyrics: “Thank you, Kanye, very cool.”
Kanye West has found himself recently embroiled in controversy over a number of antisemitic remarks. He has consequently been dropped by French fashion house Balenciaga.
The Independent has contacted a representative of Healy’s for comment.
His actions have sparked controversy online, with fans of the band condemning the singer. Others, however, have claimed that he was being “satirical” and “mocking” West over the rapper’s antisemetic statements.
“Why is no one talking about the fact Matty Healy did a H!tler salute on stage??” wrote one person, who shared the viral clip.
Another added: “Satire or not, this is irresponsible and super lame to do on stage in front of a crowd of people.”
“You cannot hide your ignorance and bigotry behind performance and dramatisation,” said a third person. “Whether it’s supposed to be satire or not, the mf willingly threw up an antisemetic sign in the middle of his performance.”
Someone else wrote: “No amount of context will ever make this behaviour OK. People who try to justify this are part of the problem too.”
“You can only hide so much under satire and art until your bigotry becomes real. context or not, a non-Jew throwing the salute is wrong. Dead wrong,” added one person.
Healey is the son of Loose Women panellist Denise Welch and actor Tim Healy.
Earlier this month, Healy attracted criticism for calling Irish people “simple” during a show in Dublin, Ireland.
At one point during the band’s performance at the city’s A3 Arena, he said: “You Irish are a simple people. You’re easily pleased. That’s good to know.”
While fans can be heard cheering and laughing after he made the remarks, some people aired their frustration at the comment on social media.