Some visitors at the National Gallery have backed the ban.
Morny Davison told the Press Association the selfie stick was "an interference in what one hopes is a reasonably calm experience looking at great pictures."
Another visitor said art lovers would be "thrilled" by the ban, adding: "They should have been banned some time ago."
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".