Her Majesty's visit, which included a keynote speech, went ahead as planned about an hour after the incident.
Gregory Pailthorpe, from Earlwood, Sydney, was arrested with an eight-inch kitchen knife strapped to his leg.
He has been charged with unlawful possession of a knife and of cannabis and was remanded to the hospital after making a brief appearance in court.
Pailthorpe was wrestled to the ground by police at Sydney's Darling Harbour Convention Centre, after he was seen to have been acting suspiciously.
He tried to get past the police by telling them he was a member of the SAS.
Police officers decided his behaviour was suspicious when they saw him try to get through a security barrier just before 0200 GMT.
Her Majesty's visit, which included a keynote speech, went ahead as planned about an hour after the incident.
Officers found an eight-inch kitchen knife strapped to the man's leg and what was described as a small improvised explosive device in his backpack.
Detective Inspector Terence Dalton, of Sydney police, described the device as a "small box with wires coming from it".
Police later said it was not capable of being detonated.
The BBC's Royal Correspondent, Nicholas Witchell, who is following the Queen's tour, says security during the visit has been discreet, but has involved a considerable number of officers.
He added that she would be continuing her programme as normal.
"It would not be in her nature to be in the slightest bit deterred or knocked off her programme by such a thing," said Mr Witchell.
He added that the "small, improvised explosive device" was not a "viable bomb", but that it was still a matter of considerable concern.
This is not the first time a member of the royal family has been at the centre of a security alert in Australia. In 1994, also in Sydney, a man ran at the Prince of Wales firing blanks from a starting pistol.
Det Insp Dalton, who is in charge of plain-clothes security, was also involved in that scare. He was the officer who arrested the man, David Kang.
There have been several small demonstrations by republicans and Aborigines since the Queen started her two-week tour of Australia.