The Kremlin-linked businessman said 23-year-old Lemekhani Nathan Nyirenda had "died a hero" fighting with Russian forces.
"Lemekhani Nathan Nyirenda on September 22 was one of the first to break into enemy trenches, showing courage and bravery," Prigozhin said through his press service on social media.
Prigozhin, whose influence has risen during the Kremlin's Ukraine offensive, said he "remembered this guy well".
The admission by Wagner boss Yevgeny Prigozhin comes two weeks after Zambia demanded an urgent explanation from Moscow over the death of its citizen.
Prigozhin recruited Nyirenda from a prison in the Tver region, north of Moscow. He claimed the Zambian willingly agreed to go and fight for Wagner.
According to Zambian authorities, Nyirenda had been studying nuclear engineering at the Moscow Engineering Physics Institute.
He had been handed a jail term in April 2020 of nine years and six months.
The authorities did not say why he had been imprisoned.
In mid-November, Lusaka had asked Russia to "urgently provide information" on the circumstances of Nyirenda's death.