Jumbo-Visma said their team leader was not showing any symptoms or feeling unwell prior to receiving his positive test.
"Clearly we're losing key pieces of the Giro". The Giro ends on October 25 with an individual time trial in Milan.
A Mitchelton-Scott were the first to withdraw after four staff members tested positive.
A Team Sunweb rider, one staff member from Ineos-Grenadiers and AG2R-La Mondiale also returned positive tests, organizers RCS said.
Jumbo-Visma said they had pulled out of the race for the safety of everyone involved.
"So the risk of passing it through to someone else has been there for several days".
The race was disrupted before the stage when the Mitchelton-Scott and Jumbo-Visma teams withdrew.
"It's like in normal life, the more tests you do the easier it is to find positives".
"That's how the situation is, we can't change anything", said Sagan.
The race was rescheduled from its usual May slot because of the coronavirus pandemic.
Vegni has suggested that the race won't have a victor if all 21 stages are not completed.
'Two and a Half Men' Star Conchata Ferrell Dead at 77
Charlie ( Charlie Sheen , left) looks on as Berta ( Conchata Ferrell , centre) holds her new grandchild on Two and Half Men. Conchata Ferrell passed away yesterday (October 12) due to complications following cardiac arrest, according to Deadline .
"This morning, all the teams that have had positive cases have undergone new quick tests and we will do the same the day after tomorrow". "We've performed almost 1500 tests and frankly it's impossible to do more than that".
Team manager Brent Copeland said: "Unfortunately we received the news on Monday evening that we have returned a number of positive COVID-19 results to members of our staff after our third round of tests in three days".
"As a social responsibility to our riders and staff, the peloton and the race organization we have made the clear decision to withdraw from the Giro d'Italia. We are now focused on safely transporting them to areas where they are most comfortable to conduct a period of quarantine".
Slovak Sagan led from the front, finally shaking off his rivals 12km from the finish line to cross alone 19sec ahead of American Brandon McNulty with Portugal's pink jersey wearer Joao Almeida third at 23sec.
The announcement of Jumbo's withdrawal was another blow for Kruijswijk, a top-five finisher in all three Grand Tours, who missed this year's Tour de France with a knee injury.
RCS, in a joint statement with the International Cycling Union (UCI), said the teams' doctors had ordered "isolation measures".
"Coming to the Giro I didn't think I'd get four stage wins. It is a very big disappointment to get this news", Kruijswijk said.
Matthews was not in overall contention - he was almost an hour behind Almeida - but he is a punchy rider and strong sprinter who was aiming for stage victories.
Team Sunweb added that the now-quarantined Matthews was also "asymptomatic, feels healthy". Four staff members but no riders tested positive for the virus that causes COVID-19 while on the French tour.
On Tuesday, the peloton, down to 145 riders from the 176 who started the race in Sicily on October 3, headed out from Lanciano for the 177km run north along the Adriatic Sea coastline to Tortoreto Lido.
"Nevertheless, that's bike racing and we'll continue to chase after our goals and I hope we can make it to Milan".