(Read more: Ahead of the Bell: Sotheby's upgraded)
The public letter calls for CEO William Ruprecht to be replaced.
"While you were an able caretaker of Sotheby's during times of crisis, you have not shown the innovation or inspiration the Company sorely needs to play offense today," Loeb wrote, also calling for the roles of CEO and chairman to be separated.
"Sotheby's requires a CEO with sufficient knowledge of the global art markets to make critical decisions, who can move seamlessly around the globe building the business and strengthening client relationships. Respectfully, we do not see evidence that you are the right person to repair the Company and drive its growth in today's dynamic global art market."
(Read more: Activist investor Dan Loeb ups Sotheby's stake)
Sotheby's didn't respond in full.
"Today, rather than debating incendiary and baseless comments, we are focused on serving our clients' needs during this critical autumn sales season, including this week in Hong Kong, where our offerings are 77% higher than the same series last year--the highest estimate of any Sotheby's sale in Asia," said spokeswoman Lauren Gioia in a statement to CNBC.com. "We will comment on the communication from Third Point at the appropriate time."
"Sotheby's actions as a leader in the global art business have been producing superior results--including a share price increase exceeding the Standard & Poor's Midcap index over the one, five and ten year periods," Gioia added. "The comprehensive capital allocation review already underway demonstrates the Company's ongoing efforts to optimize the balance sheet,improve the cost of capital and manage financial policies in a way that supports Sotheby's strategy and delivers outstanding value to shareholders."
A spokeswoman for Third Point, Elissa Doyle, declined to comment beyond the letter.
(Read more: More 'Value Investing Congress' ideas)
Loeb said that he is willing to join the company's board to help recruit new directors and change the company's direction.
Third Point's proposed fixes include revamping auctions, private and Internet sales; expanding Sotheby's global presence; and exploiting the Sotheby's brand through affiliated businesses.
"Sotheby's can also use its unique position and potential excess capital to judiciously take principal positions in works of art when doing so would not conflict with its clients' interests," Loeb added. He also pointed out what he said was wasteful pay for and spending by board members, Ruprecht and other executives.
Third Point is having another big year. The Third Point Offshore Fund rose 2.6 percent in September and is up 18.0 percent year to date,according to an investor update. The net annualized return since inception in December 1996 is a lofty 17.9%.
Other hedge funds with publicly disclosed positions in Sotheby's include Marcato Capital Management and Trian Fund Management.
—By CNBC's Lawrence Delevingne. Follow him on Twitter