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 on Friday.
While Hill says she is currently asymptomatic, her positive Covid-19 result dashes her hopes of travelling to Japan.
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."
Hill – who was due to start competing in the qualifiers this Sunday, with the final set for the following day – added on Instagram: “Broken is about the only way to describe the pain I’m feeling.”
She joins tennis pair Johanna Konta and Dan Evans in being forced to miss the Games, both announced their positive tests last week.
Another six athletes from the Team GB are self-isolating in the Olympic Village in Tokyo after sharing a flight to the city with someone who since tested positive for Covid.
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.”