President Bashir, who has been indicted by the International Criminal Court (ICC), boarded a plane shortly before a South African court was due to make its decision.
The South African government had argued against an application to arrest him on charges of war crimes and crimes against humanity over atrocities committed in the Darfur conflict.
On Sunday, a South African judge barred Bashir from leaving the country until he had made his decision.
Caroline James, the lawyer for human rights group, the Southern African Litigation Centre, said before he left South Africa that she believed there was a “real risk” he would go and the arrest application would become “mute”.
South Africa’s government challenged the application because it had given immunity to Bashir and all other delegates attending an African Union summit in Johannesburg.
The UN says as many as 300,000 people died in the Darfur conflict, with 2 million displaced. But the South African government said the ICC was unfairly focusing on African leaders and was “no longer useful”.
UN Secretary-General Ban Ki-moon said: “The International Criminal Court’s warrant for the arrest of President al-Bashir on charges of crimes against humanity and war crimes is a matter I take extremely seriously. The authority of the ICC must be respected and its decision implemented.”
South Africa is a signatory to the ICC, but the ruling African National Congress had said it wanted the court’s statutes to be reviewed to ensure a “fair and independent court”.
The ICC issued arrest warrants for Bashir in 2009 and 2010. He has rejected the court’s authority.