The cases are a first for a deployed Navy ship and are likely to pose big challenges for the crew and sea service, which is working to maintain readiness and a forward presence amid a global pandemic.
"Those individuals have been quarantined and are being flown off the ship today," Modly told reporters from the Pentagon. "... We've identified all those folks that they've had contact with, and we're quarantining them as well."
The Theodore Roosevelt Carrier Strike Group left San Diego in January for a Pacific deployment. The ship arrived in Da Nang, Vietnam, for a port visit March 5. Sailors got off the ship to participate in receptions, sports competitions, professional and other events, according to a Navy news release.
When asked why leaders approved that port call, despite reports of tens of thousands of coronavirus cases in the region, Chief of Naval Operations Adm. Michael Gilday said there were only 16 reported cases in Vietnam at the time.
"Those were well to the north and all isolated in Hanoi," Gilday said. "This was a very risk-informed decision, actually by the [head of U.S. Indo-Pacific Command Adm. Phil] Davidson, on whether or not we proceeded with that port visit."
The Navy has had coronavirus cases on ships, but the other vessels were in port. The Roosevelt is also the biggest ship to see positive cases of the coronavirus, which has caused a global pandemic, potentially leaving more Navy personnel at risk if cases begin to spread.
Modly said the ability to keep coronavirus patients -- and those with whom they had close contact -- isolated on the Roosevelt shows the Navy is combating the "pandemic with agility and professionalism."
"This is an example of our ability to keep our ships deployed at sea and underway even with active COVID-19 cases," he said. "... Our ships are sailing, our planes are flying, and training is still happening to safeguard our U.S. national interests and those of all of our allies and partners around the world."
Only sailors on the carrier exhibiting coronavirus symptoms are being tested. The ship is equipped with test kits, and the swabs are then transported to a Defense Department facility that can complete the COVID-19 checks.
Gilday declined to say where the sailors who were evacuated from the Roosevelt were transported, citing operational security. He said only that they were moved to a DoD hospital in the Asia-Pacific region.
The Navy has seen the highest number of active-duty Defense Department cases. Modly said the service currently has 57 cases among uniformed personnel. That totals nearly a third of the 174 military cases the Pentagon reported as of Tuesday morning.
Gilday said leaders have been studying ways to help stem any spread after every new positive case on a ship.
"We're taking a look at ... what kind of best practices or the do's and the don'ts that we can quickly promulgate fleetwide," he said. "I don't have a better answer [on changes yet]."