Earlier on Monday, state police had tried to move the protesters from the plaza outside the building by firing tear gas grenades into the crowd. Protesters responded by throwing rocks.
Local media reported at least 22 were injured in the clash, several of whom were journalists covering the event.
Morales' administration immediately criticised the response as excessive and fired the newly appointed state police commander just two hours after he had assumed the post.
Alicia Munoz, the government minister whose office oversees law enforcement throughout Bolivia's nine states, said the violence was an indication that Bolivia's central government must keep tighter reins on local police.
"From this moment on there will be control," Munoz said. "There will be control because we will not permit any more acts of violence or acts of repression against the social sectors who, in this case, were demonstrating peacefully."
|"There will be control because we will not permit any more acts of violence or acts of repression against the social sectors who, in this case, were demonstrating peacefully"|
Alicia Munoz, government minister
It was the third time in recent weeks that demonstrators have packed Cochabamba's tree-lined central plaza to demand the resignation of Governor Manfred Reyes Villa, a former presidential candidate who is believed to still have national political ambitions.
Last month, Reyes publicly denounced Morales' handling of an assembly rewriting Bolivia's constitution, siding with opposition leaders who say each of the new charter's articles should be written by two-thirds of the assembly's delegates.
Morales, whose Movement Toward Socialism party (MAS) holds just over half of the assembly's seats, says the charter should need the approval of the majority, with only a final draft facing a two-thirds vote.
In December, Reyes also called for Cochabamba to hold a second vote on a referendum to give Bolivia's nine states greater autonomy from Morales' central government.
The referendum was defeated in a nationwide poll in July but the autonomy issue still divides Bolivia. Cochabamba, in the Andean foothills at the centre of the country, joined four western highland states in rejecting the measure, while Bolivia's four eastern lowland states favoured it.
Both of Reyes' newly stated positions have proven distinctly unpopular in Morales' home state.