"From what I could see, just you all could see, I did not see any provocation that would warrant the deployment of munition, and especially of the purpose of movement of the president across the street", Bowser told reporters.
Washington Metropolitan police did not take part in the incident, its chief Peter Newsham said.
"We said repeatedly that we do not want the National Guard to be armed", he said.
On Monday, US federal police officers used rubber bullets and tear gas against protesters near the White House to clear a way for President Donald Trump to walk to a nearby church for a photo opportunity.
Protests have been ongoing in Washington and numerous cities in the United States after the death of African American man George Floyd in police custody in Minneapolis, Minnesota on 25 May. The protests soon turned into riots, complete with arson, looting and clashes with police.