A South African Airways flight was not allowed to take off from Zimbabwe's Harare airport on Saturday for a trip to Johannesburg in the latest row between the nations over a fistfight.
South African Airways spokesman Tlali Tlali told SABC TV that officials had asked to see certain documents that had not been requested in two decades.
In response, an Air Zimbabwe jet was denied permission to take off from Johannesburg's airport.
The countries have been at odds since Zimbabwe's first lady Grace Mugabe was prevented from leaving South Africa after allegedly beating up a 20-year-old South African woman in a Johannesburg hotel.
The 52-year-old first lady is accused of using an extension cord to whip the woman, who was there to meet with two of Mugabe's sons.
Mugabe has claimed diplomatic immunity, although she came to South Africa for private reasons, the medical treatment of an ankle injury.
There has been concern that the incident involving Mugabe, seen as a possible successor to her 93-year-old husband, President Robert Mugabe, could create a larger diplomatic crisis between the nations.
South Africa's government, meanwhile, said it had not yet decided whether to grant the Zimbabwe government's request for diplomatic immunity for Grace Mugabe, who has not commented on the allegations against her. The outspoken wife of President Robert Mugabe has been criticized for a fiery temper and lavish shopping expeditions, but her rising political profile has some asking whether she is maneuvering to succeed her husband.
There was no sign of Grace Mugabe at a regional summit that Zimbabwe's 93-year-old president attended Saturday in South Africa's capital, Pretoria.
South Africa is home to several million Zimbabweans, many of whom left their country for better opportunities, and the two countries have a close trade relationship.
Some demonstrators protested Saturday in Pretoria against Zimbabwe's president and his wife, saying she should be prosecuted.
"Arrest Grace, please. Grace is a disgrace," some chanted.
It is not clear whether Grace Mugabe entered South Africa on a personal or diplomatic passport. Zimbabwe's state-owned newspaper reported last weekend that she was in South Africa for medical care, but she told police after the alleged assault that she was scheduled to attend the summit with her husband.