Warbasse, who last raced at Il Lombardia on Saturday, is symptom-free, the team reported. He previously raced Strade Bianche, Milano-Torino and Milan-San Remo.
The 30-year-old is AG2R's second COVID-19 positive, after Silvan Dillier was forced to miss Strade Bianche after testing positive shortly before the race.
"As part of the systematic monitoring of our riders and staff, Larry Warbasse, who was symptom-free, tested positive for COVID-19," the team said in a statement.
The positive result has forced the team to isolate other riders and take precautionary measures which will impact their line-up for this weekend's French national championships. However, none of the riders affected are on AG2R La Mondiale's Tour de France long list.
"The AG2R La Mondiale team has decided to take general precautionary measures concerning certain riders and members of the staff."
The measures mean that members of the team's Il Lombardia squad will be withdrawn from racing, with Geoffrey Bouchard, Axel Domont and Ben Gastauer pulling out of the Tour du Limousin on Friday and Clément Champoussin joining Domony and Bouchard in withdrawing from the French National Championships road race on Sunday.
Warbasse is the fourth rider to test positive for COVID-19 since racing restarted in late July. As well as Dillier's positive, Astana's Hugo Houle tested positive after racing the Tour de Pologne and Israel Start-Up Nation's Omer Goldstein did so before the Vuelta a Burgos.
Given that the riders involved are not set to ride the Tour de France, Warbasse's positive test does not factor into the race's new 'two-strike' rule, which comes into effect only for those in the Tour bubble, and only from August 26.
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