The man, who had a residence permit and was believed to be a foreigner, had been bitten multiple times and was still surrounded by tigers when attendants found him, The Copenhagen Post reported.
The outdoor tiger space houses three Amur tigers, each weighing as much as about 300 pounds.
The man apparently jumped over the zoo's exterior fence during the night, and police said the zoo's after-hours security, which includes canine patrols, was adequate. Police also said none of the security guards at the zoo had seen anything unusual.
A low retaining wall and a deep moat separate the tigers from the public.
Steffen Straeder, the zoo's director, said the zoo would review the incident but had no immediate plans to change security procedures.
The tigers will not be put down, he said.
Experts say tigers in captivity normally kill their prey by biting, and the first bite typically leaves the victim unconscious. If other people are present during an attack, it's normally not fatal, the Post said.
The incident marks the first time in the zoo's 152-year history a visitor has been killed by an animal.
Lars Borg, a spokesman for the Copenhagen police, said other trespassers had climbed over the zoo's fence but were discovered by zoo patrols.