Jan Casmir Sieski, a doctor from Pennsylvania, killed a lion in April, the National Parks and Wildlife Management Authority said.
A Zimbabwean landowner has since been arrested, the agency said.
Cecil the lion was shot illegally in July by American dentist Walter Palmer of Minnesota. Zimbabwe is seeking his extradition.
The National Parks authority gave little information on the new case, but said on August 2 that the killing of the lion had taken place without a permit.
It said the hunt had been arranged by a Zimbabwean man who owned a safari company.
The authority said in a statement that it had agreed to “undertake an industry-wide investigation to crack down and weed out any illegal hunting activities”, but it was not clear if the latest case had emerged from that investigation.
A Pennsylvania address said to be Jan Casmir Sieski’s was listed in the latest release, but no further details have emerged.
Walter Palmer is believed to have paid about $50,000 to hunt Cecil, a major tourist attraction in the Hwange National Park.
The dentist says he thought the hunt was legal and was unaware Cecil was protected.
There has been a huge online backlash against Walter Palmer.
The dental practice Walter Palmer runs in Minneapolis has been closed since he was named as the hunter who shot Cecil.
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