The ship was last in port in Vietnam more than two weeks ago.
"We took great precautions when the crew came back from that shore visit, and did enhanced medical screenings of the crew", he said.
The spike in the number of cases from three earlier this week is leading the Navy to order the ship to stop in Guam, so all 5,000 sailors aboard can be tested for exposure to the virus.
"We expect additional positive tests, and those Sailors who test positive will be transported to the U.S. Naval Hospital Guam for further evaluation and treatment as necessary", he said.
A Navy official told Insider on Wednesday that the number of infected sailors had risen to eight, as five more sailors had tested positive. "We are in the process now of testing 100% of the crew of that ship to ensure that we're able to contain whatever spread might have occurred there".
"It's going to be a combination of whatever we have available for us to do that", said Modly.
By Thursday, the number of infected sailors shot up to 23, according to two USA officials.
The Roosevelt is on its way to Guam, according to Modly.
There are 5,000 sailors aboard the carrier, and Modly says some are being tested with approximately 800 test kits available and a limited laboratory capacity to process them on board.
Modly had earlier described the symptoms of infected sailors aboard the carrier as being "very mild" - namely body aches and sore throats. "Nobody from the ship will be allowed to leave the ship other than on the pier".
While seeking to shield its own forces from the virus, the Navy is also moving to ease the strain on overwhelmed hospitals during the USA epidemic.
Tara Copp is the national military and veterans affairs correspondent for McClatchy. She is the author of the award-winning book "The Warbird: Three Heroes".