The former One Direction star, 28, was due to take to the stage at the Royal Arena venue on Sunday night as part of his highly anticipated Love On Tour shows.
On Sunday afternoon, Danish police responded to a shooting at the Field's shopping centre near the arena, which is situated on the southern outskirts of the city.
Police confirmed several people were killed with others injured, while a 22-year-old Danish man has been arrested after being detained near the site.
The concert was due to begin at 8pm local time and large crowds had already gathered inside the arena when the show's cancellation was announced and they were asked to leave.
Acts such as Pearl Jam and Queen + Adam Lambert are also due to perform at the venue in the coming weeks.
Following the shooting, the Danish royal palace announced it had cancelled a reception with Crown Prince Frederik connected to the Tour de France.
The reception was due to be held on the royal yacht that is moored in Sonderborg, the town where the third stage of the race ended this year.
Styles was due to take his Love On Tour show around the world in 2020 before the pandemic brought the live music industry to a standstill.
The rescheduled tour began in September 2021 in Las Vegas before heading across the US, with the European tour leg kicking off in Glasgow last month.
Styles' most recent album, Harry's House, was warmly received by critics and lead single As It Was recently claimed its 10th week at number one in the UK.
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