The job of deputy prime minister will remain vacant while Barnaby Joyce contests a by-election to return to parliament.
Mr Joyce, who was found to be ineligible for parliament because he was a dual-citizen of New Zealand, is expected to comfortably win the seat New England at a December 2 by-election.
He renounced his New Zealand citizenship when he discovered he had it because his father was born there.
Julie Bishop will fill in as acting prime minister when Malcolm Turnbull is overseas, but neither she nor interim Nationals leader Nigel Scullion will be made deputy prime minister.
"There will be no deputy prime minister sworn in," Mr Turnbull told reporters on Saturday.
"There is an order of precedence in circumstances where the prime minister is unable to do his duties."
The traditional order of precedence is for the deputy prime minister, who is leader of the Nationals, and then the deputy leader of the Liberals and then the Leader of the Government in the Senate.
A spokesman for Senator Scullion earlier said keeping the role unfilled was in "the spirit of the (Coalition) agreement".
It's also something Barnaby Joyce expected.
Speaking to reporters in Glen Innes on Saturday, Mr Joyce was asked who should be deputy prime minister.
"Me," he quipped.
