The gallery says it has placed selfie sticks in the same category as tripods, which are banned “in order to protect paintings, individual privacy and the overall visitor experience”.
The selfie stick is an elongated pole on which a camera or mobile phone can be attached to take a better photo.
Sales of the selfie stick have soared since last year and they are now a common sight at tourist sites.
Other British institutions could also follow the ban.
The British Museum has confirmed it is reviewing its policy on selfie sticks.
A spokeswoman said: “The safety of objects and visitors is paramount to the British Museum.”
Selfie sticks are currently allowed at the National Portrait Gallery, but a spokesman said “anything that may prove disruptive is reviewed on an ongoing basis”.
“It is important that all our visitors enjoy their experience at the Gallery.”
The Tate does still allow the use of selfie sticks “provided that users respect fellow visitors and adhere to Tate’s photography policy”.
Earlier this month, the Smithsonian museum group announced it had banned selfie sticks from its 19 museums and galleries in Washington DC.
It followed similar restrictions from museums and galleries in the US including New York’s Metropolitan Museum of Art and Modern Museum of Art (MOMA), the Getty Center in Los Angeles and the Cleveland Museum of Art.
The palace of Versailles was the first museum in Europe to ban the use of selfie sticks and it is expected that The Louvre and the Pompidou centre are likely to follow suit.
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