The interior minister of the western state of North Rhine-Westphalia, Herbert Reul, said that "the limits of our tolerance have clearly been overstepped" and urged protesters to remain peaceful.
In recent days, several people were injured during demonstrations, especially in the western part of Germany.
A 50-year-old German-Turkish man was stabbed Wednesday during a Kurdish rally in the western town of Luedenscheid, while at a pro-Kurdish protest in Bottrop four people were accused of beating a man, and police were pelted with stones, the German news agency dpa reported.
Germany is home to large Turkish and Kurdish communities, and tensions between them have turned violent in the past.
Experts estimate that around one million people in Germany have Kurdish roots.
In the Netherlands, police arrested 23 protesters in the port city of Rotterdam amid clashes between rival groups sparked by a pro-Kurdish demonstration. Three officers were injured in the unrest.
Many Kurdish civilians in Syria have since left their homes to flee the violence.
Turkey views the Kurdish fighters as terrorists because of their links to a decades-long insurgency by Kurds in its southeastern territory that borders Syria.
German Chancellor Angela Merkel on Thursday once again called on Turkey to stop its military offensive in Syria, telling parliament that the attack "makes tens of thousands, among them thousands of children, flee."