The alleged incident took place around 20 nautical miles south of the Isle of Wight, just outside British territorial waters.
UK launches investigation
Responding to reports of the incident, a spokesperson for the UK Ministry of Defence said authorities were looking into the matter.
"We are investigating reports of an incident in the Channel," the spokesperson said.
A UK defence source told AFP that the episode is currently being treated as an isolated incident and is not believed to be connected to a separate operation carried out by British forces days earlier.
Yacht reports warning shots
According to the defence source, the UK-registered yacht reported that a Russian Navy vessel fired warning shots while operating approximately 500 yards away.
No injuries or damage were reported.
Following the incident, a seaboat from British naval patrol vessel HMS Tyne visited the yacht to conduct a welfare check before it continued its journey.
Officials said another Royal Navy vessel, HMS Mersey, was monitoring the Russian ship at the time.
Tensions follow UK action against Russian tanker
The reported encounter comes days after British commandos boarded the sanctioned oil tanker Smyrtos, which London says is linked to Russia's so-called shadow fleet.
The operation took place off England's southern coast in the early hours of Sunday and marked the first UK-led interdiction of a suspected Russian shadow fleet vessel.
Footage released by the Ministry of Defence showed commandos fast-roping from a helicopter onto the tanker during the nighttime operation.
Indian Captain faces sanctions charges
On Monday, British prosecutors charged Ajay Pant, the Indian captain of the Smyrtos, with violating UK sanctions imposed on Russia after its full-scale invasion of Ukraine in 2022.
Pant, 38, appeared before Southampton Magistrates' Court via videolink from a police station in Bournemouth on Tuesday.
During the hearing, he confirmed his identity and stated that he resides in India. He did not enter a plea, and his lawyer requested that the case be transferred to the Crown Court.
The court remanded Pant in custody. A plea and trial preparation hearing is scheduled at Bournemouth Crown Court on July 16.
Incident coincides with G7 pressure on Russia
The reported warning-shot incident occurred as leaders attending the G7 Summit in France agreed to increase pressure on Russia to end its more than four-year war against Ukraine.
British authorities have not yet confirmed the details of the alleged firing, and investigations remain ongoing.