Cochabamba is in central Bolivia and is home to many supporters of the former president.
Shortly after the facility was taken over by the group, the military announced the evacuation of personnel and their families, local media reported.
One of the soldiers being held in the facility said, in a message to his command centre, that the group were demanding that authorities stop interfering with blockades, Bolivian news agency ANF said.
Morales’ supporters have created blockades around the country for 19 days, demanding an end to an investigation into the former president for alleged statutory rape and human trafficking, which he denies.
On Sunday, Morales shared a video of his car being shot at, in what he called an “assassination attempt” against him.
The Bolivian government rejected Morales’ claims that it ordered a targeted attack on him.
His supporters had clashed with followers of his rival, current President Luis Arce, on several occasions earlier this year. Both men intend to run as candidate for the ruling Mas party in the country’s 2025 presidential elections.
Morales, who was president from 2006 to 2019, was declared the winner of the 2019 election but resigned weeks later after nationwide protests triggered by claims of election fraud.
