The minister, David Choquehuanca, told reporters France and Portugal had closed their airspace to the presidential plane over the "huge lie" that Snowden was on board.
Morales had been on a visit to Moscow, where Snowden -- who is facing espionage charges in the United States -- has been holed up in an airport transit area for more than a week.
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"There were unfounded rumors that Snowden may have been on board the aircraft. We have no idea who made up this huge lie."
The Bolivian leader was attending a meeting of natural gas-producing nations in Moscow and had met with Russian President Vladimir Putin.
Earlier, Morales told Russian media his country would "debate and consider" granting political asylum to Snowden "if there were a request."
Bolivia is one of 21 nations to which Snowden had applied for asylum, according to the anti-secrecy WikiLeaks website.
"Bolivia is there to shield the denounced, whether it is espionage or control. In either case, we are here to assist," Morales told Russia's state-run RT television in comments translated by the channel from Spanish.
Choquehuanca said Morales's plane had been scheduled to refuel in Portugal, but both Lisbon and then Paris denied overflight.
"Inexplicably we were informed (by Lisbon) that the overflight and landing permission had been cancelled," the top diplomat said.
The plane was re-routed to include a stop in Spain's Canary islands, but France then refused to allow overflight of its territory, Choquehuanca said.
"We would like to make it known that we are unhappy and upset because the president's life has been put in danger," he said.
Defence Minister Ruben Saavedra told Telesur news network that just an hour before entering France's airspace, the plane was told not to enter, with authorities citing unspecified technical reasons.
"They violated air traffic rights," a visibly upset Choquehuanca said, maintaining Morales' life had been in jeopardy.
"They are trying to intimidate us. This is discrimination," Choquehuanca argued.
France's foreign ministry said it could not immediately comment on the situation.
Snowden, 30, revealed details of a vast US surveillance program to collect phone and Internet data. His passport was revoked after US federal charges were filed against him.
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