Holidaymaker Natalie Bruce uploaded the footage of the encounter from a Whitby Whale Watching boat on Facebook, where it has been viewed more than 14,000 times.
In the clip, the minke whale swims close to the boat and expels water from its blowhole.
Natalie, an artist from Mirfield in West Yorkshire, was holidaying in the Whitby area when she went on a four-hour whale-watching trip.
The common minke whale can be seen off the British coast, with many tours operating from Scottish and Irish ports.
The Whitby Whale Watching trips cost £40 during the summer season.