All 100,000 copies were snapped up, publishers said - but they promised to print more copies.
The book tells the story of the king's dog, Thongdaeng, who was born as a stray but was sent to the royal palace as a gift.
Earlier this year the king sparked a fashion craze when he wore a polo shirt of the stray dog and her nine puppies.
"It just shows how much people love the king," said Visan Praweenthatsanee, a bookshop manager in the capital Bangkok.
"People have come from all around the country today, with some leaving at 5am to join the queue outside the shop."
When Thongdaeng first arrived at the palace she was reportedly very distressed, but the book says she soon settled down.
"Strangely enough, once she had been presented to His Majesty, she stopped crying, and crawled to nestle on his lap, as if to entrust her life to his care, and fell fast asleep, free from all worries, loneliness and fear," the book says.
Long-serving monarch
King Bhumibol, 74, describes Thongdaeng - an indigenous Thai dog who can pick and peel coconuts to drink the juice - as intelligent, loyal and always polite.
The king is accorded God-like status among the Thai people and they do not tolerate any criticism of him, either by themselves or outsiders.
He has been king since 1946 and is one of the most revered monarchs in Thailand's history for his hard work and devotion to his subjects.
Under laws rarely applied in recent times covering defamation of the monarchy, criticism of the royal institution is punishable by up to 15 years in jail.
There was a diplomatic row in July when a Thai restaurant in the US used an image of the king in a spoof advert.
The restaurant, in Philadelphia, was besieged by phone calls from angry Thai residents and officials when the advert showed the king as an urban hipster with bleached highlights and stone-encrusted glasses.