The cat was on the northern island of Ruegen, where most of the more than 100 wild birds infected by the H5N1 strain were found, the Friedrich Loeffler institute said.
The cat was found dead over the weekend and then tested positive for H5N1, laboratory leader Thomas Mettenleiter said.
In Geneva, World Health Organization spokeswoman Maria Cheng said this was the first time she knows of an animal other than a bird being infected in Europe. Tigers and leopards were infected by H5N1 in Thailand, where they were fed chicken carcasses in a zoo.
Bird flu infections also have been confirmed in January in humans in the Asian part of Turkey. Twenty-one people in the country tested positive for the H5N1 strain, and four children died.
It is not clear whether cats can pass the disease to humans, Cheng said.
"We know that mammals can be infected by H5N1, but we don't know what this means for humans," she said.
Mettenleiter said there are no known cases of the virus moving from cats to humans, but he still cautioned pet owners on Ruegen to keep their cats inside for now.
"An infection of humans, which theoretically cannot be ruled out, could probably only occur with very intimate contact to infected animals," Mettenleiter said.
In addition to the large cats infected in Thailand, three house cats near Bangkok were found to be infected with the virus in February 2004. In that case, officials said one cat ate a dead chicken on a farm where there was a bird flu outbreak, and the virus apparently spread to the others.
The H5N1 strain of the bird flu virus was detected in a fifth German state — Bavaria, where wild birds were infected.
The Friedrich Loeffler institute determined that two wild birds found in the southern state tested positive for the strain, state officials said.
The first cases of H5N1 in Germany were found on Ruegen in mid-February.
The World Health Organization on Monday raised its official tally of human bird flu cases worldwide to 173, including 93 deaths. Almost all human deaths from bird flu have been linked to contact with infected birds.
Meanwhile, the United States has banned poultry and live bird shipments from southeast France, where H5N1 was found in turkeys, officials said Tuesday.
However, the U.S. Department of Agriculture said the ban applies only to Ain, not to all of France. Japan and Hong Kong have suspended imports of all French poultry.