A spokesman for the Natural History Museum said it does not currently ban the use of selfie sticks and "do not currently see a need to alter our stance on this issue".
The National Museum Cardiff does not permit any camera extension devices such as tripods, and it classes selfie sticks under this category.
A spokesperson said the policy was in place "to ensure the safety of our visitors and the museum's collections, especially during crowded conditions.
"We encourage museum visitors to take selfies and share their experiences but leave the selfie sticks at home."
The BBC is awaiting confirmation from the National Galleries of Scotland to what their policy is.