The 28-year-old began to show mild symptoms following stage seven on Friday, his Mitchelton-Scott team said, and was subsequently tested at the request of their medical team.
Yates has been isolated in his hotel room and will now enter a period of quarantine.
“Simon’s health remains our main concern and, thankfully, his symptoms remain very mild & he is otherwise in good health."
Full details 👇https://t.co/SX1Hwhf8Ex
— Mitchelton-SCOTT (@MitcheltonSCOTT) October 10, 2020
Mitchelton-Scott team doctor Matteo Beltemacchi said: “Simon displayed a very mild temperature on Friday evening during our routine temperature checks, which have been completed three times per day during the course of the Giro d’Italia.
“Following the team’s Racesafe Covid-19 policy, he was isolated in his room and we immediately requested a rapid test using the services offering by the RCS, which has returned positive.”
A follow-up test confirmed the result and Dr Beltemacchi added: “Simon’s health remains our main concern and, thankfully, his symptoms remain very mild and he is otherwise in good health. We want to thank the (race organiser) RCS for their support in arranging the quick testing and his transport.”
Mitchelton-Scott said their other riders had all returned negative tests and would continue to race, but will be subject to additional testing.
Yates, the 2018 Vuelta a Espana winner, had entered the Giro as one of the pre-race favourites after his victory in Tirreno-Adriatico last month.
But he struggled on Monday’s stage three on Mount Etna, finishing more than four minutes after stage winner Jonathan Caicedo and more than three minutes down on the main group of overall contenders.
The Bury rider sat 21st overall, three minutes and 52 seconds down on race leader Joao Almeida, after Friday’s stage seven to Brindisi.
Yates’ exit means that both of Britain’s overall contenders in the race are out after Ineos Grenadiers’ Geraint Thomas suffered a fractured pelvis in a freak accident with a stray drinks bottle in the neutralised zone of stage three, withdrawing from the race a day later.
Deceuninck-QuickStep’s Almeida leads by 43 seconds from Pello Bilbao of Bahrain-McLaren going into Saturday’s 200-kilometre stage eight from Giovinazzo to Vieste.
Two-time winner Vincenzo Nibali sits fifth overall, 61 seconds down, narrowly ahead of a group of rivals including Jakob Fuglsang and Steven Kruijswijk.
Thomas’ Ineos team-mate Tao Geoghegan Hart is the best-placed Briton, 19th overall at three minutes 18 seconds down, with James Knox of Deceuninck-QuickStep a further eight seconds back.