Ten sailors were missing and five were injured following the collision, which happened at 5:24 a.m. Singapore time (5:24 p.m. ET Sunday), according to the Navy's latest update issued around nine-and-a-half hours later.
A Navy spokesman told NBC News it was being treated as an accident.
Singapore is leading search and rescue operations, providing four ships from its navy and coast guard as well as three tugboats from the Maritime and Port Authority of Singapore, its government said in a statement.
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Also involved in the effort are helicopters and Ospreys from the amphibious assault ship USS America, the U.S. Navy added.
It was not immediately clear how the USS John S. McCain, which is 505 feet in length, collided with the 600-foot Alnic MC. The destroyer was on its way to a routine port visit in Singapore at the time. The Navy said it is investigating.
The damage to the hull caused flooding to nearby rooms, including the crew's sleeping quarters and machinery and communications areas, according to the Navy. There were no reports of oil pollution in the area, according to the Singaporean government.
None of the sailors hurt suffered life-threatening injuries. Four were evacuated to the hospital by a Singaporean Navy helicopter and the fifth did not require immediate medical attention, the Navy said.
Responding to a shouted question from a reporter about the incident on Sunday, President Donald Trump said: "That's too bad," although by that point the Navy hadn't announced that the sailors were missing and it was unclear whether the president heard the question over the noise of a nearby helicopter.
Trump later tweeted that his "thoughts and prayers" were with those on board.
The guided missile destroyer is named for the Arizona’s senator’s father and grandfather, both of whom were admirals.
Cindy & I are keeping America's sailors aboard the USS John S McCain in our prayers tonight - appreciate the work of search & rescue crews https://t.co/jzk9giXbfg
The ship's three senior officers were relieved of their duties after an investigation found the sailors responsible for watching the bridge "lost situational awareness" and that "serious mistakes were made by the crew."
On May 9, USS Lake Champlain collided with a South Korea fishing boat off the Korean peninsula. And on August 19 last year, the USS Louisiana collided with the USNS Eagleview, a Navy support vessel, off the coast of Washington State. No one was injured in either incident.
CORRECTION (7:30 a.m., Aug. 22): An earlier version of this article misstated the registry of the tanker than collided with the USS John McCain. It flies under the flag of Liberia, not Libya.
Alexander Smith is a senior reporter for NBC News Digital based in London.
Ed Flanagan is a Beijing-based producer for NBC News. He has been part of the NBC News team in China since 2005 and has covered the region -- from North Korea to Japan as well.