The LCR Honda rider registered the positive test prior to flying to Argentina.
Nakagami, who has no symptoms, then took two more tests to be sure.
All were positive and the Japanese must now hope he can test negative in time to travel to next weekend's COTA round in Austin, Texas.
“Unfortunately, I will not race this weekend in Argentina," Nakagami confirmed. "I got a positive PCR test just before flying to Termas. I am really sorry for my team, sponsors and fans.
"I don’t have any symptoms and I am feeling good, I am just very sad and disappointed. I am hoping to be back on track in Austin for the Americas GP. Fingers crossed.”
Nakagami thus joins fellow Honda rider Marc Marquez in being absent from MotoGP's first visit to Termas de Rio Hondo since early 2019.
Marquez, suffering a new episode of double vision following his huge Mandalika accident, will be replaced by test rider Stefan Bradl while Alex Marquez is set to be the only LCR rider in action this weekend.
After some promising performances with the all-new RC213V in winter testing, Nakagami has finished 10th and 19th respectively at the opening rounds of this year's world championship, in Qatar and Indonesia.
Nakagami is the first premier-class rider to miss an event due to Covid since Valentino Rossi and Iker Lecuona during the latter stages of the 2020 season.
"I caught Covid on my farm [this winter]. I don't go anywhere, I don't do anything, and somehow I still managed to catch it," Miller explained. "It's quite scary as a rider, because if you're going to have to miss a race due to that, it's not nice.
"So it makes us nervous, but it is what it is."
Like Miller, Marquez and Quartararo also contracted Covid over the winter. Although it did not impact their riding duties, Miller's diagnosis forced Ducati to reschedule their team launch as he was unable to travel.
