The SAA chartered flight was part of the delegation of the African peace mission to Ukraine and Russia. President Ramaphosa flew on a separate plane, and then travelled to Ukraine on Friday via train from south-eastern Poland.
The Polish foreign ministry said some of the passengers on board the security and media aircraft were not notified to the Polish authorities ahead of time as being on board.
The Polish Border Guard said some of the president’s security detail did not have permits to carry weapons in Poland and were told they could not disembark while carrying their firearms.
Warsaw Chopin Airport spokesman Piotr Rudzki told the BBC that some of the passengers, including journalists, had now got off the plane and gone to a hotel.
“We’ve received information that they have decided to stay in Warsaw until Sunday. The journalists have disembarked, we don’t know about the other passengers,” Mr Rudzki said.
He said the aircraft had refuelled and had started to move when the cockpit informed airport staff that take-off had been cancelled and the plane would stay in Warsaw.
Earlier a South African official had said the plane would fly to Russia, where President Ramaphosa is due to meet Vladimir Putin on Saturday.
Mr Rudzki said there were passengers on board without the necessary paperwork to carry their firearms in Poland, whilst others had photocopies of their permits.
“We cannot let passengers with illegal firearms into the EU,” he said.
He said he had received information the South African authorities were in the process of sending the necessary paperwork to Warsaw.
“Some of the delegation didn’t want to be separated from their firearms. They were given the chance by the Border Guard to disembark without their firearms," he added.
"The firearms would have remained on the plane, they were not going to be confiscated as some reports in South Africa have said."
