Hill had not departed for Tokyo before her positive result was revealed.
The 23-year-old is the top-ranked women’s skeet shooter in the world and had been tipped to at least finish in the podium positions in these Games, which officially get under way with the Opening Ceremony on Friday.
While Hill says she is currently asymptomatic, her positive Covid-19 result dashes her hopes of travelling to Japan and the British Olympic Association revealed no replacement will be sent in her place.
“There are no words to describe how I’m feeling right now,” said Hill, who reached the final of her discipline at Rio 2016.
“After five years of training and preparation, I’m absolutely devastated to say that last night I received a positive Covid-19 test, meaning I’ve had to withdraw from Team GB’s shooting team.
“Although I don’t have any symptoms, I will now isolate as per the Government guidance. I will be back from this, but right now I need some time to reflect and take in what has happened.
“I would like to wish the best of luck to all of Team GB who are out in Tokyo, especially the shooting team who have supported me massively throughout my career.”
She added on Instagram: “Broken is about the only way to describe the pain I’m feeling.”
Hill becomes the third member of Team GB to be forced out of these Olympics on coronavirus grounds, with tennis pair Johanna Konta and Dan Evans announcing their positive tests last week.
Team GB’s chef de mission Mark England said: “My heart goes out to Amber, and we’re just sad for her that she is unable to join us in Tokyo.
“She is an incredibly gifted athlete and we dearly hope to see her again at a future Olympic Games.”
Hill’s rapid ascent in her sport started when she was named in the British senior team aged just 12 while she went on to become the youngest winner of a shooting World Cup title three years later.
She took silver in the 2018 Commonwealth Games and had been tipped by some to go one better in Japan.
Shooting team leader Steven Seligmann said: “This is an incredibly sad situation for Amber after she’s worked so hard to earn her Olympic place for Team GB.
“Our focus is to now make sure Amber is kept safe and well, both physically and mentally, and we have the support in place to help her through this difficult period.”
No Team GB athletes in Japan have tested positive so far, but six members of the British athletics group were earlier this week ordered to self-isolate after being identified as coming into close contact with an individual on their plane to the country who had contracted the disease.