No one was hurt, the air force said, but the incident fuelled tensions in the country where protesters have been rallying against the leftist president for two weeks.
The EC-145 helicopter “had a mechanical fault in the tail rotor during take-off, which prompted an emergency landing,” the Bolivian Air Force said in a statement.
The fault struck as the helicopter was taking off from a village in the Andes where Morales had been inaugurating a new road, it said. Videos of the incident circulated on social media.
The air force said it was investigating the causes of the fault.
On Saturday, a conservative opposition leader in the eastern Santa Cruz region, Luis Fernando Camacho, threatened to “take decisive action” on Monday night to drive Morales from power.
Former interior minister Hugo Moldiz in a Twitter message branded the helicopter incident “a criminal attack.”
Morales has accused his opponents of plotting a coup against him.
Deadly unrest has gripped the South American country since Morales was named winner of an election on October 20 for a fourth term.
His opponents have branded the result a fraud, citing alleged irregularities in the vote-count.
Morales’s rival in the polls, Carlos Mesa, has called for a new vote to be held.
Demonstrators returned to block roads in the capital La Paz on Monday in fresh protests.
In his address to supporters on Saturday, Camacho called on the military to “be on the side of the people.”
Morales responded by accusing his opponents of seeking bloodshed.
Interior Minister Carlos Romero said Monday the government had “absolute trust” in the armed forces.
Romero alleged on Sunday that “a violent confrontation is being prepared” for Monday night near the presidential palace in La Paz.