Gaviria's UAE Team Emirates said the rider "was immediately isolated following the test result and is feeling well and is completely asymptomatic."
The team noted that Gaviria also had COVID-19 in March.
Gaviria has won five stages at the Giro during his career — four in 2017 and one in 2019, plus two stages at the 2018 Tour de France.
Overall contenders Simon Yates and Steven Kruijswijk had already been withdrawn from the race after testing positive, as had Australian standout Michael Matthews. Yates' Mitchelton-Scott team and Kruijswijk's Jumbo-Visma team withdrew their entire squads last week following a series of positive results from the first rest day.
Team Emirates said all of its other riders and staff came back negative in the latest round of exams. The teams added that its medical staff is "monitoring the situation closely and doing all they can to ensure the we can proceed safely."
Italy added another 10,874 confirmed coronavirus infections to its official toll Tuesday. The government has implemented new restrictions to curb nightlife and socializing in hopes of slowing the resurging outbreak.
Another 89 people died, bringing Italy's official COVID-19 death toll to 36,705, the second highest in Europe after Britain.
Portuguese rider João Almeida leads the race by 17 seconds ahead of Dutch rival Wilco Kelderman.
- AP