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"If a team has two positive cases or (members) with strong symptoms within a seven-day period, they will be out of the race," Amaury Sport Organisation (ASO) said in a statement to Reuters.
Team managers aren't happy with the strict ruling and will meet with ASO representatives on Tuesday evening (AEST) to further clarify the protocols, according to L’Equipe.
"Kicking off a team if two of its members test positive is a radical decision," manager of B&B Hotels-Vital Concept team Jerome Pineau told L’Equipe.
"I do not think much of the peloton will make it to Paris."
"If a mechanic or a bus driver are declared positive, without symptoms, I dare to hope they will be quarantined without stopping everything."
Earlier, sports directors who will be on the event running until Sept. 20 confirmed a report by cycling website Velonews that the race would be over for teams who are found to have two infected members in their ranks.
"The measure was announced to us at the Criterium du Dauphine," one sports director, who declined to be named because he is not authorised to discuss the matter, told Reuters.
The Critérium du Dauphiné is also organised by ASO, who used the week-long race earlier this month as a dress rehearsal for the Tour de France.
Riders and team staff will be in a bubble from the day they arrive in Nice ahead of the Grand Depart on Saturday.
They will be tested for the coronavirus twice before the race starts, and a mobile testing lab will be at their disposal.
Dutch rider Inge van der Heijden withdrew from the Dutch national championships after she tested positive for coronavirus ahead of the race also forcing two of her team mates Yara Kastelijn and Aniek van Alphen due to safety protocols.
However, in a post on her Instagram account on Sunday (AEST), van der Heijden said she had another test on Saturday 22 August which returned a negative result.
The former under 23 Cyclo-Cross world champion said she expected that result as she was not displaying any symptoms and her first PCR (Polymerase chain reaction) test on Friday 14 August was also negative, her second PCR on Wednesday returning the positive result which forced her withdrawal.
Team INEOS was forced to withdraw all of its riders from the road race at the Italian National Championships after Leonardo Basso returned a positive result to a test on Saturday 22 August. Gianni Moscon, Filippo Ganna, and Salvatore Puccio and four staff members will also self-isolate for 14 days.
"He has been and remains asymptomatic," the team statement said.
"Apart from a visit for treatment on his knee at his local medical centre eight days ago, Leonardo has been at home in Asolo with his girlfriend and training alone over the last 10 days.
"He tested negative on Tuesday. He has remained at home and did not join the team at their hotel in recent days. However, he carried out the time trial recon with Filippo Ganna yesterday and went on a training ride with him, Salvatore Puccio and Gianni Moscon this morning."
Tour director Christian Prudhomme told Reuters on Thursday a rider testing positive for the coronavirus would be required to isolate, along with his room mate, but that it would not lead to the race being abandoned.
France has seen a surge in COVID-19 cases recently, although the number of hospitalised people has remained stable.