In the clip captured by Natalie Bruce, 48, the juvenile minke can be seen twisting and turning ‘like a dancer in the sea’ before spraying water from its blowhole.
The 48-year-old uploaded footage of the chance encounter during her maiden voyage out to sea on Facebook, where it has been viewed more than 14,000 times.
The part-time artist says staff at Whitby Whale Watching were ‘shocked’ to see how close the majestic animal got to the boat.
Mother-of-two Natalie, from Mirfield, West Yorkshire, had booked the £40 boat tour on August 27 as an early birthday present for her daughter Natasha Aldred.
Around an hour into the sun-kissed trip, Natalie along with the 10 other passengers spotted the whale in the distance off the east coast of Yorkshire at midday.
Seconds later the curious minke got ‘closer and closer’ before surfacing next to the boat where it came and said hello to stunned whale watchers.
The minke began shooting air from its blowhole and submergeing into the water before splashing around and showing its underbelly as it twist and turned.
She said: “It was my daughter’s birthday present, we thought we would only see a couple of whales from a distance.
“All of a sudden one minke whale got closer and closer and came right up to the boat and started playing with us.
“It was tossing and turning, it was showing off really. It kept on spraying water and going underneath the boat from one side to another.
“It was a decent size and the other people on the boat could not believe it. It’s the first time I have been on a boat trip.
“The weather was immaculate and we could not have asked for a better day.
“Staff were shocked to see how close the minke whale got to the whale. It must have known it was Natasha’s birthday and came over to celebrate.”
Birthday girl Natasha, 27, wrote a touching post on her blog ‘prettylittleearththing’ about the experience.
She said: “All the crew and ourselves couldn’t believe our luck. What we experienced from this one whale was astonishing.
“Seeing it’s white fins, and underbelly as it twisted and turned. Showing off it’s full body like a dancer in the sea.
“Then letting off one massive bubble before swimming away, now named Mr Bubbles.”
For the rest of the four-hour trip, the group were followed by playful seals, porpoises and larger whales as they swam in the distance.
The North Sea is one of the few places the common Minke whale can be spotted in the UK. They can deep dive for up to 20 minutes and can swim up to 24mph.
In the summer and autumn months, minke whales make regular appearances along the east coast of Yorkshire following the shoals of mackerel and herring.