There was no indication the man's actions were linked to terrorism, Berlin police spokesman Winfrid Wenzel said.
The dpa news agency quoted police as saying the man appeared to be confused.
Mr Wenzel said the incident began when the man entered the Berliner Dom and waved a knife in the area of the altar.
Cathedral employees called police and dozens of people were evacuated from the holy site.
One of the two officers responding to the call opened fire, wounding the man, Mr Wenzel said.
The second officer was inadvertently wounded by the shot or shots fired by his colleague, Berlin police said.
Both the suspect and the police officer were taken to hospital. Dpa said the officer is in serious condition.
The area around the cathedral is typically crowded with tourists and visitors, particularly on Sunday. A Sunday evening prayer service at the church was cancelled.
Reporting by Associated Press.
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