The US 7th Fleet said a helicopter was preparing to land on the USS Chancellorsville when the Russian destroyer, travelling behind the US ship, speeded up and approached as close as 15-30 metres.
It accused the Russian destroyer of putting the safety of the Chancellorsville and its crew at risk, forcing it to reverse all engines at full throttle to avoid a collision.
A spokesman for the Japan-based 7th Fleet said no one was injured and he was not aware of any damage to the ship.
In turn, the Russian military accused the Chancellorsville of making a dangerous manoeuvre by crossing the path of the Russian destroyer Admiral Vinogradov in the open ocean, northeast of the Philippines.
It said in a statement that the US cruiser "suddenly changed direction and crossed the path of Admiral Vinogradov just 50 meters (165 feet) away", forcing the crew of the Russian ship to make a quick manoeuvre to avoid collision.
The Russian military said its navy sent a radio message in protest.
It was the first such incident involving warships in the region since September, when a Chinese ship manoeuvred close to an American destroyer in the South China Sea , an incident the US also labelled unprofessional and unsafe.
The US repeatedly complained in recent years that Russian planes flew dangerously close to American aircraft and the two nations routinely shadow each other in international airspace.