Despite winning their final game of the season 2-1, Hamburg were sent down by Wolfsburg’s 4-1 home win over Cologne.
When relegation was confirmed, fans set off flares and police and security staff came on to the pitch.
The match was completed after a 10-minute delay at the Volksparkstadion.
Hamburg, who needed to win and for Wolfsburg to lose, had been the only team to play every season in the Bundesliga since its 1963 formation.
Aaron Hunt put them ahead with a penalty awarded by the video assistant referee for handball, before Josip Drmic equalised.
Lewis Holtby scored Hamburg’s winner from 16 yards, while Bobby Wood was sent off.
Hamburg, who narrowly stayed up for the past four seasons, enjoyed a revival towards the end of the season under caretaker boss Christian Titz, winning four of his eight games.
They join Cologne in being relegated to the second tier, while Wolfsburg play Holstein Kiel in the promotion-relegation play-off.
Holstein Kiel were only promoted from the third tier in 2017 and were playing regional football in 2012-13.