"Children who eat such meat often may suffer a small reduction in IQ," Catherine Svindland of the FSA said. "Lead affects the development of the central nervous system."
The FSA commissioned the report from Norway's Scientific Committee for Food, which found that the amount of lead found in neat varied enormously from as little as 0.03 milligrams per kilogram up to 110 milligrams.
The report, which is being published at the start of Norway's Elk-hunting season, advises that children, pregnant women and individuals with high blood pressure should not eat too much game meat.
Eskil Pettersen, county Secretary for the Norwegian Hunting and Fishing Association in Sør-Trøndelag, whose family eats deer every week said he was troubled by the report.
"I find it hard to believe it, but we have to believe it when the FSA is behind it," he said, adding that his children did not seem any less intelligent than others.