But law enforcement officials said there was no threat to the public and the fire was not believed to be a threat to the inauguration.
Local firefighters put out the blaze quickly.
The evacuation of some participants and the lockdown were ordered by the acting chief of Capitol Police in an abundance of caution, officials said.
Mr Biden was not participating in the rehearsal, nor were other VIPs who will attend Wednesday’s ceremony.
But the fast decision to lock down underscores the fear that has gripped Washington since the deadly Jan. 6 insurrection at the US Capitol by pro-Trump rioters and prompted extraordinary measures ahead of the inauguration.
Armed protests planned for this past weekend around the country were mostly a bust, but anxiety is still skyrocketing.
US Secret Service tightened security in and around the Capitol a week early in preparation, and the city centre is essentially on lockdown with streets blocked, high fencing installed and tens of thousands of National Guard and other law enforcement officers stationed around the area.
But US defence officials, worried about a potential insider attack or other threat from service members involved in securing the event, pushed the FBI to vet all of the 25,000 National Guard troops coming into the area.
President Donald Trump has refused to attend the inauguration, the first time a sitting president has not attended since Andrew Jackson, though Vice President Mike Pence will be there as well as other former presidents.
Capitol police spokeswoman Eva Malecki said there were currently no fires on or within the campus.
“Members and staff were advised to shelter in place while the incident is being investigated,” she said in a statement.
Participants were ushered from the West Front of the Capitol.
Those who had gathered for a walk-through, including a military band, were directed to head indoors and moved in the direction of a secure location inside the Capitol complex.
People involved in the rehearsal said security officials yelled “this is not a drill”.
The lockdown was lifted about an hour later.
Five people died in the January 6 riot, including a police officer.