"What we are experiencing constitutes an act of the Turkish regime's coercion. It no longer follows the rule of law and has nothing to do with democracy," Deutsche Welle boss Peter Limbourg wrote on the broadcaster's website.
Recorded on Monday, the interview with Youth and Sports Minister Akif Cagatay Kilic included "questions which had been divulged to the ministry in advance", on issues such as the failed July 15th coup, the post-putsch crackdown, press freedom and women's rights, Deutsche Welle said.
But according to the broadcaster, the minister changed his mind straight after the interview was conducted at his Ankara office.
The minister's spokesman told the two journalists that they were not allowed to broadcast the footage, while ministry employees confiscated the recording.
"It was made clear to the TV crew that they would not be able to leave the ministry in possession of the video footage," the broadcaster said.
Deutsche Welle has since made several appeals for the footage to be returned, but the sports minister refused.
The broadcaster is now considering legal action, it said.
In a statement on its website, the Turkish Ministry of Youth and Sports confirmed an incident had taken place but denied any wrongdoing, shifting the blame to the German broadcaster.
It said that the Deutsche Welle interviewer had "overstepped the mark with expressions and accusations" and as a result the ministry had asked the outlet not to broadcast the interview.
Defending the decision, it claimed that such a move was in line with a policy of "authorisation" for interviews that also existed in Germany.
The incident follows a wave of tension between Ankara and Berlin after the German parliament passed a resolution in June recognising the World War I-era massacres of Armenians by Ottoman forces as "genocide".
Berlin has also spoken out against Turkey's tough line against critical journalists and in the standoff against Kurdish militants as well as the mass arrests that followed July's failed coup.