This is the second time the same Russian vessel has come within close proximity of a US Navy ship this month.
On June 17, the Yaroslav Mudryy came within 288 metres of the USS Gravely, an incident US officials called "unsafe and unprofessional", but which the Russian Defence Ministry disputed.
Recent months have seen a number of similar Cold War-style incidents at sea and in the air, with each country's military accusing the other of dangerous approaches in international waters and airspace.
The US Defence official, who was speaking on the condition of anonymity, said the most recent incident took place on June 30 when the Yaroslav Mudryy came unnecessarily close to the USS San Jacinto and manoeuvred in its wake.
"The closing distance by Yaroslav Mudryy before the ship turned away from San Jacinto is considered a high-risk manoeuvrer, highly unprofessional, and contrary to international maritime regulations," the official said.
The official added however, that the US guided-missile cruiser was never threatened by the manoeuvrers.
"Conducting aggressive, erratic manoeuvrers and moving unnecessarily close to another ship in open ocean is inconsistent with prudent seamanship," the official said.
At the time of the incident, the San Jacinto was carrying out operations against Islamic State militants in Iraq and Syria with the USS Dwight D Eisenhower, the official said.
In another incident in April, the US military said Russian SU-24 bombers had simulated attack passes near the USS Donald Cook in the Baltic Sea, with one official describing them as one of the most aggressive interactions in recent memory.
US Secretary of State John Kerry said at the time that the behaviour of the Russian pilots was provocative and dangerous, adding that "under the rules of engagement that could have been a shoot-down".