Video shows the approximately seven metre long mammal soaring effortlessly out of the water several times on the clear sunny day.
The enormous sea creature glides out of the water head first and soars high into the air just metres away from the boat that Struan works on.
It then rotates mid flight before plummeting back down into the water making a gigantic splash.
Coastal Connection, a boat tour service run by Struan and his twin brother Cameron Smith, shared the video on their Facebook on Monday.
The post read: “Struan had an incredible encounter today. A breaching minke whale north of Staffa.”
The video has attracted over 18,000 views and hundreds of likes.
Viewers were left in awe by the amazing sighting.
Tony Hammock said: “Fantastic! It’s very difficult to catch them with a camera when they are breaching.”
Nikki Wasik said: “That’s incredible!”
Betty Graham said: “Wow that is awesome.”
Helen Sloan said: “Oh that’s incredible, how lucky to see that guys.”
Speaking today, Struan, 36, from Oban, Argyll and Bute, said: “We’re always on the look out for whales, dolphins and sharks.
“We saw a splash or a break in the wash and thought there shouldn’t be any rocks there as we were quite deep.
“We locked on to it and watched it breach around nine times, landing on its front mostly but on its back too.
“That one (in the video) was probably the peak of them to be honest.
“We’ve heard about it and other people have seen it but I’ve never really myself.
“Minkes are usually quite sneaky and don’t usually breach like that.
“I was quite surprised because I’d never seen it before, you do get minkes down there but it’s not usually a hotspot.”
Minke whales reach lengths of up to 35 feet long and weigh up to 20,000 pounds.
Female minkes tend to be larger than their male counterparts.