Cardinal Joachim Meisner was speaking at the blessing of his archdiocese's new art museum, the Kolumba, in the heart of Cologne, on Friday.
"Wherever culture is separated from the worship of God, the cult atrophies in ritualism and culture becomes degenerate," he said.
The word "degenerate" is hardly ever used in Germany today because of its known association with the Third Reich.
The National Socialists' aggressive persecution of artists whose works did not conform to their ideology culminated in 1937 with the infamous Munich-exhibition called "Degenerate Art" in which a collection of modernist artworks was displayed, accompanied by texts deriding the works.
"Appalling" choice of words
"It's appalling that Cardinal Meisner uses such words and it shows he knows nothing about art and culture," said Hans-Heinrich Grosse-Brockhoff, North Rhine-Westphalia's secretary of culture.
The 73-year-old cardinal initially defended his choice of vocabulary, but his office issued a statement on Saturday saying he regretted that some of his words had been taken out of context and that he was shocked by the public reaction.
"Cardinal Meisner rejects allegations that he was linking himself to a term which was abused by the Nazis," read the statement.
Freedom of expression?
Former cultural minister of North Rhine-Westphalia Michael Vesper also condemned Meisner's use of Nazi terminology.
"I am shocked that the term 'degenerate' is still used," Vesper told the daily newspaper Express. "I thought that was history in Germany,"
"Art is free and should not be pocketed by anyone. Anyone, like Cardinal Meisner, who is prepared to reject art which does not fit into his own pigeonhole of thought ... is stoking a dangerous fire," he told Express newspaper.
Meisner already caused controversy earlier this month by criticizing the abstract stained glass windows designed for Cologne Cathedral as something that "belongs to a mosque or another place of prayer but not this one."
Meisner is the second prominent figure in Germany this week to draw fire for alluding to subjects linked to the Third Reich.
Last Sunday, Germany's public television networked fired popular talkhost Eva Herman after she praised the way family values were nurtured in the Third Reich.
Writer Ralph Giordano said he didn't think that Meisner wanted to establish a positive link to the epoch of National Socialism, but that the wording of his statement was inappropriate.
"In terms of the mindset, some things still carry over from that epoch, and it would've been better if Cardinal Meisner had not used this word," Giordano said.