England and South Africa are in Afghanistan's group in the one-day international competition and under pressure to boycott the fixtures in response to the Taliban government's crackdown on women's rights since returning to power in August 2021.
South Africa are scheduled to open their Champions Trophy campaign against Afghanistan in Karachi on February 21 but McKenzie urged his country's cricket governing body not to honour the fixture.
"Cricket South Africa, the federations of other countries and the ICC (International Cricket Council) will have to think carefully about the message the sport of cricket wishes to send the world, and especially the women in sports," he said in a statement on Thursday.
"It is not for me as the Sports Minister to make the final decision on whether South Africa should honour cricketing fixtures against Afghanistan. If it was my decision, then it certainly would not happen.
"As a man who comes from a race that was not allowed equal access to sporting opportunities during Apartheid, it would be hypocritical and immoral to look the other way today when the same is being done towards women anywhere in the world," he added.
Cricket South Africa responded with a statement on Thursday, saying they would take their lead from the ICC, and that a "unified and collective approach from all ICC members" was needed.
"CSA finds the treatment and suppression of women's rights in Afghanistan abhorrent and firmly believes that women's cricket deserves equal recognition and resources," the statement said.
"As the Champions Trophy is an ICC event, the position on Afghanistan must be guided by the world body in accordance with international tournament participation requirements and regulations."
More than 160 British politicians have signed a cross-party letter to the England and Wales Cricket Board, calling for a boycott of England's fixture against Afghanistan in Lahore on February 26.
ECB chief executive Richard Gould responded by also calling for a uniform approach from all member nations towards Afghanistan's participation in international cricket.
Australia are the other country scheduled to take on Afghanistan, in Lahore on February 28.
Cricket Australia indefinitely postponed a bilateral men's Twenty 20 series against Afghanistan last March citing "deteriorating human rights for women and girls in the country under Taliban rule".
But they did play them at the World Cup in India in late 2023 and at the T20 World Cup last June.
Cricket Australia chairman Mike Baird last month said he was "very proud of the position we've taken" after they were accused of hypocrisy.
"We've taken a position, and we're proudly standing up where we think we should," he said.
