Russia's Pacific Fleet said the cruiser USS Chancellorsville passed just 50m (160ft) in front of the destroyer Admiral Vinogradov at 06:35 Moscow time (03:35 GMT).
It said it was forced to perform "emergency manoeuvring" to avoid the US ship.
But US forces blamed the Russians, claiming their ship was responsible.
US Seventh Fleet Commander Clayton Doss called the Russians "unsafe and unprofessional", saying their destroyer "made an unsafe manoeuvre against USS Chancellorsville". He dismissed the Russian allegation as "propaganda".
Admiral Vinogradov came within 50 to 100 feet (15m-30m) of the USS Chancellorsville in the Philippine Sea, the US said.
The Russian Pacific Fleet meanwhile said the incident took place in the southeast of the East China Sea, and added they had sent a message of protest to the US ship's commanders.
In a statement it said the US warship had "suddenly changed direction and crossed the path of Admiral Vinogradov just 50m away," forcing the Russian crew to make a quick manoeuvre.
The US said later that it would lodge a formal diplomatic complaint, or demarche, with Russia over its warship's movements.
"We'll have military-to-military conversations with the Russians, and of course we'll demarche them," acting Defence Secretary Patrick Shanahan told reporters.
Both countries regularly accuse the other of dangerous military manoeuvres - at sea and in the air.
In November, the US posted footage of a Russian jet intercepting one of its planes over the Black Sea - a move they called "irresponsible", but which the Russians said was to stop "a violation of Russian airspace".