A home video of a Scottish grandmother’s uncontrollable giggles while reading The Wonky Donkey picture book to her baby grandson have sent book lovers around the world rushing to get their hands on a copy, with publishers left scrambling to meet demand.

New Zealander Craig Smith’s children’s book, based on Smith’s song of the same name, tells of a three-legged – or wonky – donkey, adding a new adjective every few pages until it ends with a “spunky, hanky-panky cranky stinky dinky lanky honky-tonky winky wonky donkey”. In a recent video made by her daughter, Scottish granny Janice Clark reads the story to her four-month-old grandson Archer, and laughs progressively harder as the donkey becomes increasingly bizarre. “Oh dear, how can anybody read this seriously,” says Clark. “This is going to kill me.” The video has been viewed more than 3m times in the last week.

Smith told the Guardian that demand had “gone through the roof” for the picture book since the video of Clark took off: in New Zealand, his publisher is “rushing to print another 50,000 copies, with a view for more”, while The Wonky Donkey is now also being reprinted in the UK. Amazon in the US and the UK has sold out, while used bookseller AbeBooks said that it has sold “hundreds of copies” of The Wonky Donkey in the last week, amid “massive demand” around the world.

Although the picture book, which is illustrated by Katz Cowley, had sold more than 1m copies around the world to date, the majority of that was in Australia and New Zealand, said Smith, who hopes it will find a more global readership.

“The video is gold. Watching Janice read and laugh was just delightful, and like many, her infectious laugh had me laughing too,” said Smith. “I’ve always wondered why sales had not taken off so much in the UK and US, but that looks like that’s about to change.”

Cowley said that while The Wonky Donkey has been a household name in Australia and New Zealand since it was first published in 2009, the book had been only “an underground success” in the UK.

“I am so glad that Wonky’s reputation has finally come to bite him on the bum on this side of the world thanks to ‘Wonky’s Guardian Granny’. I couldn’t be more delighted,” Cowley said, calling Clark “a reminder in life, when all else fails, to fall about laughing. She has a spirit like Wonky’s.”

At Hachette, which publishes the book in the UK, group picture book director Emma Layfield said the publisher had already seen a “well-deserved jump in demand” for the book, “especially in Scotland”.

“It’s delightful to see the infectious appeal of Wonky Donkey spread around the globe. The video is a fantastic demonstration that the best picture books entertain the whole family, not just the kids,” said Layfield.