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 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.
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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".
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.
After the latest incident today, a major search and rescue operation was launched, with planes and vessels from Singapore, Malaysia and the US involved.
"They are already out there, they have already arrived," he told AFP.
The rescue operation also involved tug boats, a helicopter and a police coast guard vessel from Singapore, and US aircraft were responding, 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.
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