The five-piece rock band from Sheffield played at Alexandra Palace in North London on Friday when the incident occurred.
BMTH posted a message of condolence on their Twitter page.
It read: “Words cannot express how horrified we are feeling this evening after hearing about the death of a young man at our show last night.
“Our hearts and deepest condolences go out to his family and loved ones at this terrible time.
“We will comment further in due course.”
The circumstances surrounding the man’s death are not yet known but eyewitness reports claim a man was carried out of the crowd in the 10,000-capacity venue by security and was treated by paramedics.
Alexandra Palace said in a post on the social networking site: “A medical incident occurred at last night’s Bring Me The Horizon concert.
"Our thoughts and condolences are with the individual's family and we would like to express our deepest sympathy to them.
"We hope you can appreciate we cannot provide any further comment at this time.”
Online comments have raised questions about security arrangements on the night.
One gig goer, who did not want to be named, told The Sun Online: “I was very scared. I decided to leave early."
However the venue has moved to stop speculation about security.
In a later Twitter message it wrote: “Following the above statement, we would like to clarify that this was a tragic medical incident and unrelated to the extensive security measures in place.
"However, we feel we must address inaccurate information. There were over 150 security personnel on site for the concert.”
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