The Netwerk24 website said an elephant cow stormed a group headed by Theunis Botha in Zimbabwe on Friday.
The elephant was reportedly shot as she picked him up with her trunk, before she fell and died, crushing Mr Botha.
He had been leading a group of hunters near the Hwange national park in Zimbabwe when he died.
It is the same park where Cecil the Lion was shot dead by an American hunter in July 2015, sparking an international outcry.
Mr Botha, 51, was a father of five from the northern Limpopo province in South Africa.
His eldest daughter Marike confirmed her father’s death to the BBC, but would not comment further on the circumstances of his death.