The guided-missile destroyer USS John S. McCain collided with the merchant vessel Alnic MC near the Straits of Malacca in the early hours, the US Navy said.
"Initial reports indicate John S. McCain sustained damage to her port side aft," it said in a statement as the ship headed to port in Singapore.
"There are currently 10 sailors missing and five injured... Search and rescue efforts are underway in coordination with local authorities.
"The extent of damage and personnel injuries is being determined. The incident will be investigated."
Four of the injured sailors were evacuated from the warship to a Singapore hospital by helicopter with non-life-threatening injuries while the fifth did not require further medical attention, the navy said.
The navy said the destroyer was sailing under its own power after the collision with the Liberian-flagged tanker in Malaysian waters at 5.24 am as it headed for a routine stop in Singapore.
The vessel is named after US Senator John McCain's father and grandfather, who were both admirals in the US navy.
McCain said in a tweet that he and his wife "are keeping America's sailors aboard the USS John S McCain in our prayers tonight - appreciate the work of search & rescue crews".
President Donald Trump initially said "that's too bad" in response to reporters' shouted questions about the collision, as he arrived back at the White House after a holiday.
He followed up with a tweet: "Thoughts & prayers are w/ our @USNavy sailors aboard the #USSJohnSMcCain where search & rescue efforts are underway."
It was the second collision in recent times involving a US warship after seven sailors died in June when the destroyer USS Fitzgerald collided with a Philippine-flagged cargo ship in a busy channel in Japan.
Air-sea search
After the latest incident on Monday, a major search and rescue operation was launched, with planes and vessels from Singapore, Malaysia and the US involved.
Singapore sent three tugboats, and four navy and police coastguard vessels while Malaysia – whose southern Johor state was close to the collision – deployed eight ships and said it was going to send aircraft to help in the search.
A US helicopter was taking part in the search and two other American aircraft were expected to arrive soon, the navy said.
The ship involved in the accident is a Liberian-flagged tanker used for transporting oil and chemicals and weighing over 30,000 tonnes, according to industry website Marine Traffic.
In the June accident, the collision happened in a busy channel not far from Yokosuka, a gateway to container ports in the Japanese capital Tokyo and nearby Yokohama.
The dead sailors, aged 19 to 37, were found by divers in flooded sleeping berths a day after the collision tore a huge gash in the side of the Fitzgerald.
A senior admiral announced last week that the commander of the destroyer and several other officers were relieved of their duties aboard their ship over the incident.
There have been around 30 ship collisions over the past decade in that area, including a 2013 incident in which six Japanese crew died, according to the Japan Coast Guard.
The USS John S. McCain is part of the US Seventh Fleet, and its home base is Yokosuka, in Japan.
