The fire broke out at the Eisenhower Executive Office building, located near the West Wing of the White House and housing presidential staff members.
A White House press secretary said the fire appeared to have started in an electrical closet or telephone bank.
One person suffered a minor hand injury. Neither the president nor the vice-president were affected.
Vice-president's office
EISENHOWER BUILDING
Firefighters entered the building to tackle the blaze and were seen breaking windows and removing furniture.
The fire broke out near Mr Cheney's ceremonial office.
Mr Cheney himself was in the West Wing of the White House with President George W Bush at the time, officials said.
The White House was not evacuated, but hundreds of staff members were forced to leave the Eisenhower Building.
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