Tony Evers made the move after protesters also threw a Molotov cocktail into a government building and a state senator said he was attacked.
One of the statues pulled down was of an anti-slavery US Civil War hero.
The violence from a group of between 200 and 300 people first broke out on Tuesday night as crowds protested against the arrest of a black man who shouted at restaurant customers through a megaphone while carrying a baseball bat.
Officers used pepper spray to repel protesters who were trying to gain entry into the historic centre of state government, Madison police said.
After touring the damage on Wednesday, Mr Evers said: “What happened in Madison last night presented a stark contrast from the peaceful protests we have seen across our state in recent weeks, including significant damage to state property.”
The violence exposed simmering anger over the 2015 shooting by police of a 19-year-old black man by an officer who was eventually cleared and remains on the force. That shooting has been referenced by protesters in recent weeks.
The violence started after Madison police arrested a protester who came to a restaurant with a baseball bat on his shoulder.
Video released by Madison police shows the man, Devenore Johnson, talking through a megaphone while walking around the restaurant’s outdoor patio. He walks inside and paces through the restaurant with the bat on his shoulder, saying he’s “disturbing” the restaurant before walking out.