McGrath told the Australian selectors he wanted to stay in Australia to be with his family while his wife undergoes treatment for cancer.
Cricket Australia released a statement saying they fully supported McGrath's decision. The Test squad to tour South Africa will be announced next week.
McGrath, 36, pulled out of Australia's triangular One-day series at home last month as well as the limited-overs series in South Africa after revealing his wife had been diagnosed with cancer and needed immediate radiotherapy treatment.
McGrath's English-born wife Jane has twice been diagnosed with cancer before. She was diagnosed with breast cancer in 1997 then bone cancer in 2003 but made a full recovery on both occasions.
Australia and South Africa are to play three Tests starting in Cape Town on Mar.16.