The visitors center — where tourists go through security and begin their guided tours of the domed building — however remained closed to the public.
Congress was in recess Monday for the Easter holiday, but it is a busy week for tourists in Washington, with the city's famed flowering cherry trees in full bloom.
Many school groups visit Washington during the week after Easter.
CNN and MSNBC reported that the suspect had been shot and taken to hospital.
Police cordoned off access to the Capitol building during the incident. An ambulance was at the scene. "There has been an isolated incident at the US Capitol. There is no active threat to the public," Washington police said on Twitter.
The White House — where thousands were attending the annual Easter Egg Roll — was briefly on lockdown as well, apparently after someone tried to scale the fence, but the order was quickly lifted.