Cheney's office was damaged by smoke and water from fire hoses, White House spokesman Scott Stanzel said. The vice president was not in the building at the time; he was in the West Wing of the White House with President Bush.
CBS News White House correspondent Mark Knoller reports the historic desk in the vice president's ceremonial office is said to be covered with soot - but sustained no fire damage.
The desk was first used by Theordore Roosevelt in 1902. It was used by every Vice President since LBJ - and inside of the top drawer has been signed by various users since the 1940s.
More than 1,000 people who work in the building were evacuated. The fire broke out on the second floor of the building around about 9:15 a.m. and was under control within a half hour, District of Columbia fire department spokesman Alan Etter said.
Afterward, Mr. Bush and Cheney appeared on West Executive Avenue, between the White House and the damaged building, to thank District of Columbia firefighters. A fire tanker nearby still had its ladder extended to a window on the blackened second floor.
The blaze was located in Cheney's suite of ceremonial offices. His working office is in the West Wing. Secret Service spokesman Darrin Blackford said the building was evacuated as a precaution. District of Columbia firefighters poured water on the blaze, broke windows and moved furniture onto a balcony.
There were no reports of serious injuries, Etter said. A U.S. Marine stationed at the building smashed a fifth-floor window to escape from the smoke and had to be rescued from the ledge, he said. The man suffered a minor cut to his hand.
The building remained evacuated while firefighters ventilated the smoke, Etter said. The displaced employees were sent to other offices or went home.
The extent of water, fire and smoke damage was unclear.
Investigators were working to determine the cause of the blaze, Etter said. The smoke appeared to come from an electrical closet on the building's second floor.
The Executive Office Building, a commanding structure with a granite, slate and cast iron exterior at the corner of Pennsylvania Avenue and 17th Street, houses the Office of Management and Budget and staff of the National Security Council and other agencies.
Originally built for the State, War and Navy Departments between 1871 and 1888, the building was renamed in honor of President Dwight Eisenhower during the Clinton administration.