A crowd of 62,200 turned up at the Allianz Arena for the relegation play-off against Jahn Regensburg.
The tie was poised at 1-1 after the first leg but 1860 Munich conceded twice in the first half and go down.
Play was suspended for around 15 minutes and police said 10 officers had been "slightly injured" due to trouble.
1860 Munich were champions of Germany in 1966 - two years after winning the German Cup.
They lost to West Ham United in the final of the 1965 European Cup Winners' Cup in front of a 97,000 crowd at Wembley.
In February, Liverpool chief executive Ian Ayre left to join 1860 Munich after 10 years at Anfield.
However, it was revealed after Tuesday's relegation that Ayre had left his role as general manager.
1860 Munich have not been in the Bundesliga since 2004, and lost 3-1 on aggregate to Leeds United in the third qualifying round of the Champions League in 2000.
This season, they finished 16th in the 18-team second tier after losing 18 of their 34 league games.
Jahn Regensburg are promoted to Germany's second tier.
Ten police officers were injured as former Bundesliga champions 1860 Munich were relegated to Germany's third tier in a game held up by crowd trouble.