Thousands of people poured on to the streets of Kampala, outraged by the fires.
Witnesses say at least one person was killed, after the military fired on the crowds.
It is not clear what started the fire at the Unesco-listed tomb site.
The 19th Century structure was a burial site for kings of the Buganda region.
The kingdom has had uneasy relations with the central government recently.
Witnesses say Ugandan President Yoweri Museveni tried to visit the tombs.
But crowds blocked his convoy.
A dispute over territory between the regional king and the President led to mass riots last year.