State-owned television network TV7 said a pro-Morales demonstrator was killed during the clashes.
It was not immediately clear how he was killed. Local radio Erbol reported that police were trying to break up the protest with tear gas.
Thousands of supporters
Thousands of Morales supporters gathered in the main square of Cochabamba, 275 miles (440 km) east of La Paz, on Thursday, hours before supporters of Reyes Villa entered the city, also armed with batons and rocks, local media reported.
"I don't have a reason to resign, I demand the will of my voters be respected," Reyes Villa, who is one of Bolivia's first elected governors, told ATB television network.
"Autonomy is important. It doesn't mean division, or separatism, or independence. Why are they still concentrating power?
The regional governors have been elected, let's give them some power," Reyes Villa told reporters. Regional leaders were appointed by the president until 2005.
Anti-Reyes Villa protesters had blocked off roads to Cochabamba for three days. Earlier this week, Morales backers set fire to the governor's office, sparking scuffles with the police that injured more than 20 people.