Five PKK fighters approached the camp and chose three people to kidnap, Cetin said.
Agri province, which borders Iran, is to the north of the main PKK conflict region and is a popular destination for mountain climbers.
"The terrorists said they carried out this action because of the German government's recent moves against PKK associations and sympathisers," the governor was quoted as saying.
Last month the German interior minister banned Kurdish television station Roj TV, which was described as being a mouthpiece for the PKK.
Germany extradited two PKK activists to Turkey last year.
A German foreign ministry spokesman told reporters the ministry and German embassy in Ankara were urgently pursuing the reports about the kidnapping.
"The embassy is in close contact with Turkish authorities," a spokesman said.
Cetin said gendarmerie forces were carrying out search operations in the region. The other climbers were taken to the nearest town.
The PKK, considered a terrorist organisation by Turkey, the United States and the European union, took up arms against the Turkish state in 1984 with the aim of establishing an ethnic homeland in southeast Turkey.