The 190-strong company aboard the HMS St Albans set sail on December 23 to monitor the Russian Admiral Gorshkov frigate and tracked its progress through what the Royal Navy called areas of national interest on Monday.
The Navy said there had been a recent "upsurge" in Russian units travelling through UK waters, including on Christmas Eve when HMS Tyne was called to escort a Russian intelligence-gathering ship through the North Sea and the English Channel.
A Wildcat helicopter from 815 Naval Air Squadron, based at RNAS Yeovilton, was also scrambled to track two other Russian vessels.
HMS St Albans will return to Portsmouth on Boxing Day.
Commander Chris Ansell, the commanding officer of the Type 23 frigate, said: "My ship's company take great pride in serving Great Britain and the role they play dealing with both the routine and unexpected.
"Missing parts of Christmas and New Year with our families is never easy, but it is absolutely required as part of our duty to keep Britain safe all year round.
"Christmas Eve saw some particularly exciting and bumpy weather, with some of my newer sailors getting used to their sea legs, but we have made sure the job was done and I will get my team back home as soon as possible.
"Our families have been incredibly supportive and even sneaked a few presents into our bags so we had things to open, resulting in a great Christmas Day at sea."
The crew are among around 4,000 sailors deployed or on standby across the world, the Royal Navy said.
Defence Secretary Gavin Williamson 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."