In the southwestern city of Freiburg, about 4500 people joined a demonstration against a proposed vaccination mandate and other measures to contain the pandemic, police said on Saturday. Organisers had expected about 7000 participants.
Police said there were no incidents of note, although counter-demonstrators had tried to block the route of the march with bicycles.
In the eastern city of Leipzig, police put an end to a demonstration attended by several hundred people.
A spokesperson said a few dozen people broke through a police cordon and ran onto the grounds of the psychiatric ward of Leipzig University Hospital, where the police detained them to establish their identities.
Police said investigations were under way - among other things, for violating the assembly act, resisting law enforcement officers and violating coronavirus rules in the state of Saxony.
Elsewhere in the state, up to 1250 people gathered for an unauthorised protest in the town of Zwonitz, police said.
Ten people's details were taken down because they had disguised their faces - an offence at public gatherings in Germany. In addition, authorities have launched an investigation into the demonstration for not being registered beforehand.
In Brandenburg an der Havel, a town west of Berlin, police broke up an unregistered demonstration against coronavirus policies. Participants faced charges for joining an unauthorised gathering or not following mask-wearing rules.
Several hundred people also demonstrated in Schwerin in the northeastern state of Mecklenburg-Vorpommern on Saturday. At its peak, the gathering had around 900 people, according to police.
There were other events linked to the pandemic, for example in the town of Cuxhaven on Germany's North Sea coast, where about 1250 people formed a socially distanced human chain stretching 2.5 kilometres, a spokesperson for the local authority said.
The stunt was meant as a showing of solidarity.
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