Statues of Churchill, heralded as the leader who halted the spread of Nazism and led the UK to victory in the Second World War, and the Cenotaph, a memorial to the First World War dead have both been vandalised during the protests.
They are now being protected with a boards and scaffolding to prevent further attacks.
A statue of slave trader Edward Colston was torn down in Bristol and thrown into the harbour.
The incidents have led to discussion around which historical figures are appropriate to celebrate through monuments, with a number of statues across the UK being targeted by protestors.
There have been calls to remove statues in Northern Ireland, including one in Newry of John Mitchel, who is said to have supported the slave trade in 1800s America.
Scaffolders erect boarding around the Cenotaph on Whitehall (Kirsty O’Connor/PA)
Mrs Foster said she thought it was "incredibly sad" that the Cenotaph in London had to be boarded up to protect it from vandalism.
"The fact that we have to protect the statue of one of our greatest leaders, Winston Churchill, in the fashion that we have and the way in which it was attacked last week," the First Minister said.
"People need to reflect on the fact that we're living in the 21st century, we're living in a totally different era and we have different values than certainly in Oliver Cromwell's time and in the 18th and 19th centuries.
"I think it's wrong to erase history, obviously we have to have a balance, look back at history to realise what has happened in the past and where we are today and the progress that has been made."
The Fermanagh and South Tyrone MLA said she understood the reason for the protests, but not for the attacks on the monuments.
"I do think it's wrong, I can understand the desire of people to protest about the death of George Floyd in America and the Black Lives Matter protests, but to attack cultural icons such as Winston Churchill I think is an incredibly sad indictment of where the United Kingdom is today."
Mrs Foster also defended Scouts founder Robert Baden-Powell.
Bournemouth, Christchurch and Poole Council had originally said it would temporarily remove his statue after it was featured on a 'hit-list' compiled by protesters.
However the removal has been delayed after local residents vowed to protect it.
Protesters have targeted the monument over Baden-Powell's associations with the Nazis and the Hitler Youth programme, as well as his actions in the military.
"As a former Girl Guide leader and member of the Girl Guide organisation I know the good that Baden-Powell's organisation has done right across the world and I think it's so sad to see his statue having to be protected by members of the scouting movement at this time," Mrs Foster said.