Yates, who was in 21st place, nearly four minutes down on race leader Joao Almeida of Deceuninck-Quickstep, developed mild symptoms at the conclusion of Stage 7 on Friday evening before he returned a positive test.
However, the team will race on after all other riders and staff members returned negative tests.
"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," Mitchelton-Scott doctor Matteo Beltemacchi said.
"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.
"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 RCS for their support in arranging the quick testing and his transport.
"All other riders and staff have returned negative results and have been cleared to continue the race, but as a precautionary measure we will monitor the situation closely and undergo further testing in the coming days.”