Morales had earlier met with Russian President Vladimir Putin at a summit of major gas exporters in the Kremlin.
In an interview with Russia Today television, Morales said that his South American country would be willing to consider granting asylum to Snowden.
Leaks by Snowden, a former NSA systems analyst, have revealed the NSA's sweeping data collection of U.S. phone records and some Internet traffic, though U.S. intelligence officials have said the programs are aimed at targeting foreigners and terrorist suspects mostly overseas.
He is believed to be in a Moscow airport transit area, seeking asylum from one of more than a dozen countries.
"This is a hostile act by the United States State Department which has used various European governments," said Bolivian Defense Minister Ruben Saavedra, who was on the flight.
Choquehuanca said in a statement that after France and Portugal canceled authorization for the flight, Spain's government allowed the plane to be refueled in its territory. From there the Falcon plane flew on to Vienna.
He said the decision by France and Portugal "put at risk the life of the president."
Morales was in the Vienna airport Tuesday night meeting with the plane's crew to reprogram his return to Bolivia, the defense minister Saavedra said.
Snowden has applied for asylum in Venezuela, Bolivia and 18 other countries, according to WikiLeaks, a secret spilling website that has been advising him. Many European countries on the list -- including Austria, Finland, Ireland, the Netherlands, Norway, Spain and Switzerland -- said he would have to make his request on their soil.
WikiLeaks said requests have also been made to Brazil, China, Cuba, Ecuador, France, Iceland, India, Italy and Nicaragua.
One of Snowden's best chances of finding refuge outside the United States may hinge on the president of Venezuela, Nicolas Maduro, who was also in Russia on Tuesday.
Maduro told Russian reporters that his country has not received an application for asylum from Snowden and dodged the question of whether he would take him with him when he left.
But Maduro also defended the former National Security Agency systems analyst.
"Who must protect Snowden? This is the question. This young man of 29 was brave enough to say that we need to protect the world from the American imperial elite, so who should protect him?" Maduro said in response to a question from journalists covering a ceremony to rename a Moscow street after Chavez. "All of mankind, people all over the world must protect him."
Maduro was scheduled to spend Wednesday in neighboring Belarus before returning to Venezuela.
In Venezuela, Foreign Minister Elias Jaua condemned the decision by France and Portugal.
"All the countries that have denied permission for the flight of our brother president, Evo Morales, must be held responsible for his life and his dignity as president."
Snowden, who recently turned 30, withdrew a bid for asylum in Russia when he learned the terms Moscow had set out, according to Putin's spokesman Dmitry Peskov. Putin said on Monday that Russia was ready to shelter Snowden as long as he stopped leaking U.S. secrets.
At the same time, Putin said he had no plans to turn over Snowden to the United States.