Vincent van Gogh’s Sunflowers, John Constable’s The Hay Wain and Diego Velazquez’s Rokeby Venus have all been damaged.
The spokesperson said: “Such attacks have caused physical damage to the artworks, distress to visitors and staff, and disruption to our mission to ensure great art is available for everyone, everywhere to enjoy.
“Two of these attacks have happened in the last two weeks and that is why we have taken the difficult and unfortunate decision to change the way we operate for the foreseeable future.
The gallery advised visitors to take “minimal items” with them, and said all bags would be inspected.