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.
An autograph book containing a sketch of a shark drawn by Damien Hirst has sold for £4,664 at auction.