Speaking from Windsor Castle, the monarch has held a video call with the governor of South Australia, Hieu Van Le, and the premier Steven Marshall.
"I would think possibly it might be quite alarming to suddenly see it out of the window - you'd think, gracious, has she arrived unexpectedly?" the monarch remarked on seeing the statue.
The sculpture, which depicts the Queen in a coat and hat carrying her trademark Launer handbag, has been installed in the grounds of Government House in Adelaide.
Told it had become the most popular place for people to take photographs, the Queen chuckled and said: "Oh really?"
"They feel very close to you through standing in front of the statue," Mr Le said.
The monarch's video call, which took place last Wednesday, was released by Buckingham Palace on Monday local time, the same day the Duke of Edinburgh was transferred to another hospital by ambulance.
Philip, 99, had spent almost two weeks in King Edward VII's hospital, and was moved to St Bartholomew's for testing and observation for a pre-existing heart condition.
Sculptor Robert Hannaford also presented the Queen with a 'maquette', a scale model of the statue, which will be sent as a memento.
"That's very kind," the Queen remarked. "I'm glad it's not quite as big as the original statue."
At the start of the call, the monarch joked about what time of day it was in Australia.
"Good morning," she said. "Well that's good morning to me. It looks ... I don't know what time of day it is to you."
The Queen was briefed by the governor and premier on developments in the region, including the vaccination rollout to key workers, the response to COVID-19 and the lifting of restrictions in South Australia.
The Queen also heard about the recovery from drought and bushfires and the co-operation between health services, police, government - and the resilience of the Australian people.
It was her first video call to Australia and Buckingham Palace said it was the first time the Queen had unveiled a statue virtually.
The royals have switched the majority of their official engagements online during the coronavirus pandemic, with the Queen staying at Windsor Castle for her safety during lockdown.