Palmer had paid $55,000 to killed Cecil, a black-maned lion who had become a star attraction at Hwange National Park. Cecil was also wearing a tracking collar for an Oxford University research project.
Zimbabwe officials said they would investigate the act after widespread outrage around the world. However, Environment Minister Oppah Muchinguri said her country will drop its bid to bring Palmer to justice because the dentist was visiting the country legally.
She added that they would look into the process by which hunting visits are granted.
"We are now going to review how we issue hunting quotas," she said, noting that Palmer would not be permitted to hunt in Zimbabwe in the future.
The Minnesota-based dentist apologized for killing 13-year-old Cecil, saying he believed it was legal hunt, having been misled by his guide, professional Zimbabwean hunter Theo Bronkhorst, who remains charged with "failing to prevent an illegal hunt."