The incident -- separate from the killing of Cecil the lion in July -- involved an allegedly illegal hunt put on by a safari guide who has been arrested for his role in it. The U.S. man, a doctor from Pennsylvania, had hired the guide, Zimbabwe's Parks and Wildlife Management Authority said.
CNN is not naming the doctor, who has not been charged. Zimbabwe also has not requested his extradition.
The man has not yet commented on the statement.
The Zimbabwean government did not say what species of animals were hunted in the allegedly illegal safari, which authorities say was conducted without a quota or permit.
Officials have vowed to crack down on illegal hunting in the wake of the July death of Cecil. Authorities have ordered the suspension of hunts targeting lions, leopards and elephants outside of Hwange National Park amid a broad investigation into hunting industry practices. The latest accusations emerged during the inquiry, the authority said.
Cecil was a major tourist draw at Hwange, as well as the subject of a long-running research study. His death brought widespread condemnation of Palmer, and the practice of hunting lions and other big game trophy in general and prompted Zimbabwe to demand his extradition
Palmer, his professional hunter guide and the owner of the land where the hunt took place are accused of taking part in an illegal hunt, according to the government.
Palmer is accused of financing an illegal hunt, and he and the professional hunter are accused of illegally using a bow and arrow to avoid detection by park rangers, Oppah Muchinguri, the African nation's environment minister, said last week. They are also accused of using food to lure Cecil out of the protected game reserve before killing him.
The landowner allegedly allowed the hunt to be conducted without a lion quota and without the necessary permit, Muchinguri said.
Palmer has said he relied on the expertise of local guides "to ensure a legal hunt."
"I had no idea that the lion I took was a known, local favorite, was collared and part of a study until the end of the hunt," Palmer said in a statement last week.
U.S. officials have declined to comment on Zimbabwe's extradition request.
On Sunday, researchers in Zimbabwe rejected reports
of the death of another male lion with whom Cecil had formed a close bond. Jericho was alive and well, Oxford University researchers said, tweeting a photo as proof.
Although sometimes referred to as brothers, Cecil and Jericho were in fact unrelated males who had formed a "cooperative coalition" to fend off rivals, Oxford researcher David Macdonald said.
Jericho is apparently caring for and defending Cecil's 24 cubs, researchers say. The survivability of those cubs would have been imperiled if Jericho had indeed been killed, according to experts.