Following the latest incident, Defence Secretary Gavin Williamson said the UK would “never be intimidated” when it came to protecting the country.
It comes just days after Foreign Secretary Boris Johnson clashed with his Russian counterpart Sergei Lavrov over alleged cyber attacks on the West and activity in Ukraine.
Portsmouth-based HMS St Albans set sail on 23 December and remained at sea on Christmas Day to keep track of the Russian frigate “in areas of national interest”, the MoD said.
On Christmas Eve, patrol ship HMS Tyne was called to escort a Russian intelligence-gathering ship travelling through the North Sea and the English Channel.
A Royal Navy Wildcat helicopter was also dispatched to monitor another two Russian vessels during the festive period.
Mr Williamson, who is reportedly fighting cuts to the MoD budget, said: “I will not hesitate in defending our waters or tolerate any form of aggression.
“Britain will never be intimidated when it comes to protecting our country, our people, and our national interests.”
Chris Ansell, the commanding officer of HMS St Albans, said: “There is a pressing need to protect UK interests close to home, in the air, above and below the waves.
“Our trade, economy and information networks depend on the sea, and this operation demonstrates the Royal Navy’s commitment to protecting our home waters and readiness to undertake short notice operations.”
The 190-strong company on board HMS St Albans are due to return to Portsmouth on Boxing Day.