The protests on Saturday followed a wave of 'Gen Z'-led demonstrations across Europe.
In Serbia, student-led activism helped unseat the country's longtime leader at the ballot box, while protests in France have descended into rioting and looting.
The German protests organised by the campaign group "Gen Z regelt" - "Gen Z takes charge" in German - took place in 34 cities including Berlin, Frankfurt and Munich. The group says it opposes compulsory military service and wants greater investment in education as many young Germans struggle with rising costs.
In Frankfurt, Germany's financial hub, at least two stores were looted as protests turned violent, with several more damaged and police trying to get the situation under control, according to a Reuters witness.
"Violent disturbances are continuing," Frankfurt police said on X.
"In the city centre, windows have been smashed at several shops. Molotov cocktails are also being thrown at the emergency services. We urge all bystanders to avoid the city centre or to leave the area."
Official numbers on Saturday afternoon suggested turnout was below the 182,000 participants that organisers initially expected.
Police in Frankfurt, Munich and Berlin reported as many as 18,000 protesters, half the roughly 36,000 on the organisers' website.
German authorities said Saturday's demonstrations, which coincide with Halloween festivities, had been largely peaceful, but warned of attempts by extremist groups to exploit the movement.
In Hamburg, some barricades were set on fire.
Parts of Germany's far-left extremist scene and some groups linked to foreign extremist movements have joined efforts to mobilise support, according to the federal interior ministry.
Some businesses across German cities boarded up windows and planned early closures ahead of the demonstrations due to concerns over possible unrest, including along Berlin's luxury Kurfuerstendamm shopping boulevard.
Organisers have focused on what they see as the growing pressure on younger generations in Europe's largest economy.
Germany has struggled to revive economic growth. The country also faces growing pressure on pensions and public services as baby boomers retire and the working-age population shrinks.
Questions have been raised about who is driving the campaign and whether it is genuinely youth-led, given the broad mix of political and civil society groups involved.
