"We condemn the permission given for the organisation of an activity by the PKK (Kurdistan Workers Party) terror group's extensions in Germany and their spreading terror propaganda there today in Cologne," the ministry said in the statement.
"We have expressed our reaction in a strong way to Germany's ambassador to Ankara who was summoned to the ministry," it added.
The statement criticised German authorities for allowing the PKK's imprisoned leader Abdullah Ocalan's posters to be unfurled and group leaders' messages to be read out during the rally.
German-Turkish ties have plunged to an all-time low since last year's failed coup against President Recep Tayyip Erdogan and the subsequent crackdown in Turkey which has seen more than 50,000 people arrested.
Relations further deteriorated after the detention of several German citizens including Deniz Yucel, a correspondent for Die Welt newspaper, prompting Berlin to announce a full review of relations and to sharpen its travel advisory.
Erdogan has in return accused Germany of sheltering coup plotters, as well as Kurdish militants, and demanded their extradition.
The Turkish foreign ministry on Saturday said Germany's "double standard approach is worrying in the global fight against terror."
"We are inviting Germany to demonstrate a principled approach against all forms of terror," it added.
The outlawed PKK has waged an insurgency in Kurdish majority southeast Turkey since 1984.