Kurds and Alevis, a moderate Islamic sect who make up 20 percent of Turkey's population, said they were demonstrating "for democracy, peace and freedom" and against sweeping purges by Turkish authorities since the failed July coup.
Some held up pictures of jailed Kurdistan Workers Party (PKK) leader Abdullah Ocalan, detained since 1999 on the prison island of Imrali, off the coast of Istanbul.
Others held portraits of Selahattin Demirtas, the young co-leader of the People's Democratic Party (HDP), arrested last week with several other members of the pro-Kurdish group accused by Erdogan of being a front for the PKK.
Cologne police reported a group of young Kurdish troublemakers at the edge of the demonstration.
"Flares were ignited by a few individuals. When police tried to prevent them, stones and other objects were thrown at them," said a police statement.
One policeman suffered an injured hand and one protestor was detained, according to DPA.
Germany is home to about 1 million Kurds, more than any other European country, as well as the world's largest Turkish diaspora community, and fears of tension between them on German soil are fuelled by Erdogan's repression.