The 41-year-old Italian said he could also miss next week's Teruel Grand Prix at the same circuit in Spain.
"Unfortunately, this morning I woke up and I was not feeling good. My bones were sore and I had a slight fever, so I immediately called the doctor who tested me twice," said Rossi in a statement.
"The quick PCR test result was negative, just like the test I underwent on Tuesday.
"But the second one, of which the result was sent to me at 16:00 this afternoon, was unfortunately positive. I am so disappointed that I will have to miss the race at Aragon."
Rossi, in his final season with the factory Yamaha team, had endured a tough season with three successive crashes leaving 'The Doctor' down in 13th in the world championship.
"I'd like to be optimistic and confident, but I expect the second round in Aragon to be a 'no-go' for me as well... I am sad and angry because I did my best to respect the protocol and although the test I had on Tuesday was negative, I self-isolated since my arrival from Le Mans," he added.
"Anyway, this is the way it is, and I can't do anything to change the situation. I will now follow the medical advice, and I just hope I will be feeling well soon."
Rossi's absence is another setback for the factory Yamaha team after six of their technical staff missed last week's race at Le Mans when one member tested positive – despite being asymptomatic.
"These two incidents remind us that no matter how careful you are, the risk is always present - as we see with the rising numbers of infections in Europe at this time," said Yamaha team managing director Lin Jarvis.
Rossi's condition will be closely monitored by medical staff in Tavullia, Italy, where he lives.
"We have checked with the Italian health authorities and we have been advised that any member of our team that was in contact with Valentino up until Monday is excluded from direct risk," added Jarvis.
"Nevertheless, we will be even more attentive from now on to minimise the chance for any future issues."