Malcolm Turnbull. Photo Reuters
Former prime minister Tony Abbott's reinstatement of the honours, which led to a knighthood being given to Prince Philip, was used against him by critics to show how out of touch he was with public attitudes.
The change won't impact existing knights and dames of the order.
Shadow Treasurer Chris Bowen said the honours should never have been brought back in the first place.
"It was a farce, a joke, a national disgrace," he told reporters in Sydney.
Greens Leader Richard Di Natale welcomed ditching knights and dames, but said Australians deserve more from the new prime minister.
"I'm pretty underwhelmed that Malcolm Turnbull's first big break from Tony Abbott is on the matter of honorifics," he said in a statement.
