The doodle references the artist's famous work of a tiger shark pickled in formaldehyde and was given to an unnamed chauffeur as a tip.
"A great drive," wrote the artist along the top of the page.
The sale came in the same week that critic Julian Spalding said Hirst's work was "not art" and the market for his productions would bottom out.
"The emperor has nothing on," he told The Independent. "When the penny drops that these are not art, it's all going to collapse."
However, the sale of the Hirst sketch appears to show that some collectors continue to value his output.
It was bought by an anonymous bidder during a sale at International Autograph Auctions in London on Saturday, 24 March.
Alongside Hirst's sketch, the autograph book also contained signatures from the likes of Alan Bennett, Julie Walters, Alastair Campbell and Ricky Gervais.
Comedian David Baddiel also signed the book, writing: "To Peter, It won't be worth as much as the Damien Hirst."
The collection was originally valued at £250-350.
An exhibition catalogue signed by Damien Hirst also sold for £900 at the same auction. A spokesman for the auction house said an unadorned page bearing the artist's inscription would normally raise about £100.
The highest-value lot at the auction was a signed photograph of Marylin Monroe.
It was originally given to Jack Cole, who was the star's choreographer on Gentlemen Prefer Blondes.
Monroe scrawled across the picture in light blue ink: "Jack - You certainly can - and I'm not mad! Marilyn".
The photo was sold for £20,088, including VAT and buyer's premium.

Wenger's side have developed an unwanted reputation for failing to win the league from promising positions.
However, he believes Arsenal are better placed now as there is no squad unrest.
"When we went into April in 2010, some of the players were tapped up to go somewhere else and it was difficult to maintain the focus," he said.
"That's not the case at the moment."
Arsenal - who are five points behind leaders Leicester going into Sunday's game at Manchester United - last won the Premier League in 2004, when they went through the 38-game campaign without defeat.
They were runners-up to Chelsea the following season, and have finished either third or fourth every year since.
A number of significant challenges for the title in the last 12 years have failed to bring the Premier League trophy to the club.
In February 2008, they were five points clear of Manchester United with 12 games left, but were derailed by a 2-2 draw at Birmingham in which striker Eduardo suffered a bad leg break and captain William Gallas remained sitting on the pitch at full-time in a public show of anger.
Two seasons later, Wenger's side were top of the table with seven matches to play, but won only two of those games and finished third.
They were in a strong position to push Manchester United in 2010/11, but began to crumble in February as they let slip a four-goal lead in drawing 4-4 at Newcastle, and ended up dropping from second place to fourth.
And two seasons ago, Arsenal were top in early February, but a 5-1 defeat at Liverpool began a run of just two wins in nine matches, and they again ended in fourth place.
"What is different is that at that time we were losing momentum," Wenger said. "This time it's the opposite.
"Also we were very young at that time, with the famous incident with Gallas at Birmingham. And the mood of some players was more to get the next contract somewhere else than to win the championship because at the time we had to sell our players.
"Now we do not have that problem. All the players are focused and want to win and have great solidarity. It's down to showing how good we are. The psychological situation is completely different today than it was in 2010.
"In 2010, I would say we lost it because the spirit was not exactly what it should be because of individual tap ups. At the moment, on the spirit front we are all right."
An autograph book containing a sketch of a shark drawn by Damien Hirst has sold for £4,664 at auction.
[NEXT_CONCEPT]
Some of Arsenal's recent Premier League title challenges have been damaged by their players being approached by other clubs, manager Arsene Wenger says.