Since Bashir was indicted by the ICC in 2009 over alleged war crimes and crimes against humanity during the Darfur conflict, his overseas travel has been severely restricted.
"Bashir left for Johannesburg at the head of the Sudanese delegation taking part in the African Union summit," SUNA reported.
His top adviser Bakri Hassan Salih and several ministers were at the airport for his departure, SUNA added, without saying exactly when he left.
Since his indictment Bashir has mostly travelled to countries that have not joined the ICC.
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The court relies on signatories to its founding treaty to arrest indictees.
Darfur erupted into conflict in 2003 when ethnic insurgents mounted a campaign against Bashir's government, complaining their region was politically and economically marginalised.
More than 300,000 people have been killed in the conflict and fighting has forced some 2.5 million people to flee their homes, the United Nations says.
Khartoum estimates the death toll from the conflict at 10,000.