The National Parks and Wildlife Management Authority said a doctor from Pennsylvania, named as Jan Casimir Seski, killed a lion in April.
A Zimbabwean landowner has since been arrested, the agency said.
Cecil was shot illegally in July by US dentist Walter Palmer of Minnesota. Zimbabwe is seeking his extradition.
The Associated Press news agency says Mr Seski is a gynaecological oncologist who runs the Center for Bloodless Medicine and Surgery at Allegheny General Hospital in Pittsburgh.
The agency called at his home, in woods outside Pittsburgh, and left a telephone message but received no response.
Images on websites linked to hunting show a “Dr Jan Seski” standing next to dead animals including elephants, an impala, a hippo and an ostrich, the agency added.
The National Parks authority gave little information on the new case, but said on Sunday 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.
Mr Palmer is believed to have paid about $50,000 (£32,000) to hunt Cecil, a major tourist attraction in the Hwange National Park.
He says he thought the hunt was legal and was unaware Cecil was protected.
There has been a huge online backlash against Mr Palmer.
The dental practice he runs in Minneapolis has been closed since he was named as the hunter who shot Cecil.
On Thursday, the White House said it would review a public petition to extradite the American dentist after more than 100,000 signed it.
But spokesman Josh Earnest said it was up to the US justice department to respond to any extradition order.