After flirting with relegation in recent seasons, Hamburg needed a win and a favor from already relegated Cologne against Wolfsburg to maintain hope of another escape.
Hamburg fans staged protests at the Volksparkstadion following club's first relegation from Bundesliga since its formation in 1963.
Wolfsburg's 4-1 mauling of Cologne meant that Hamburg's 2-1 home win over Borussia Moenchengladbach on Saturday, wouldn't have been enough to kee them in the top flight.
Wolfsburg will face Holstein Kiel in the promotion-relegation play-off.
Dozens of riot police, several on horses, charged onto the pitch and lined up in front of the Hamburg fans, who lit several flares and threw them behind the Gladbach goal when it became clear that the team was on its way to the second division.
Some Hamburg players broke down and cried after referee Felix Brych finally ended the game after a long hold-up due to the disturbances.
Borussia Dortmund were made to sweat until the last seconds to secure the final Champions League spot after losing 3-1 at Hoffenheim, who grabbed third place ahead of them on goal difference.
Stuttgart produced arguably the performance of the day, hammering Bayern Munich 4-1 at the Allianz Arena to leapfrog Eintracht Frankfurt - who lost 1-0 at Schalke - into seventh.
League president Reinhard Rauball handed the trophy to goalkeeper Manuel Neuer, who has not played since September previous year due to injury and faces a race against time to be fit for the World Cup.
That placing will see Stuttgart join Leverkusen and Leipzig in the Europa League, providing Frankfurt do not overcome Bayern in next weekend's DFB-Pokal final.
The victor qualifies for the Europa League, but Bayern has already reached the Champions League.
Also, Werder Bremen won at Mainz 2-1.