His extradition was being sought so that he could “be held accountable for his illegal action,” she said.
Walter Palmer, from Minnesota, is believed to have paid about $50,000 to hunt the lion.
He says he thought the hunt was legal and was unaware Cecil was protected.
At a news conference in the capital, Harare, Oppah Muchinguri referred to Walter Palmer as a “foreign poacher”.
“As we frantically try to protect our wildlife from organized gangs such as this one, there are people… who can connive to undermine Zimbabwean laws,” she said.
“One can conclude with confidence that Dr Palmer, being an American citizen, had a well-orchestrated agenda which would tarnish the image of Zimbabwe and further strain the relationship between Zimbabwe and the USA,” Oppah Muchinguri added.
She also said Walter Palmer’s use of a bow and arrow against Cecil was in contravention of Zimbabwean hunting regulations, Reuters reports.
Two Zimbabwean men have been implicated in the death of the lion.
A professional hunter has been charged with failing to prevent an illegal hunt – which he denies – and prosecutors are deciding on the exact charges the landowner should face.
There has been a huge online backlash against Walter Palmer. The dental practice he runs in Minneapolis has been closed since he was named as the hunter who shot Cecil.
On July 30, the White House said it would review a public petition to extradite the American dentist after more than 100,000 signed it.
However, spokesman Josh Earnest said it was up to the DoJ to respond to any extradition order.
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