The first minister said there needs to be a "balanced conversation" about the removal of statues across the UK.
Arlene Foster said she understands the desire to protest but said she was sad to see memorials and statues being boarded up.
She said it was "incredibly sad to see the Cenotaph boarded up" in London.
A statue in London of former British prime minister Winston Churchill was vandalised with graffiti declaring him a "racist".
Speaking on ITV's Good Morning Britain programme, Mrs Foster described Mr Churchill as "one of our greatest leaders".
She said it was "wrong to erase history" and said it was important to have a "balanced conversation".
She also said, as a former girl guide leader, that she praised the work of Lord Baden Powell, who formed the scouting movement.
His statue is to be removed from Poole Quay amid fears it is on a target list for attack.
Mrs Foster said his organisation had done good "right across the world".