Three people were also reported missing, according to the national bureau of natural catastrophes (BNGRC), which did not provide any other details.
Earlier it was reported that only one person had been killed when the storm passed over Madagascar last week before lashing the coasts of South Africa and Mozambique, where at least one person was killed.
"A tree fell on a house and the roof collapsed," killing an elderly man in Mozambique's southern Gaza province, said Rita Almeida, spokeswoman for the national disaster agency.
In the South African city of Durban, beaches were closed as waves reached a height of three metres (16 feet), municipal spokesman Thabo Mofokeng said. Ships were ordered to remain in port.
Irina was the second killer storm of the season. Last month, tropical cyclone Giovanna left 35 people dead and many more injured.
Madagascar's cyclone season normally runs from November through February and costs dozens of lives every year.
The worst in recent decades hit southern Africa in January 1984, killing 214 people and causing heavy damage.
