The Latvian army, without saying who launched the drone, said it entered from Russia "as a result of Russian electromagnetic warfare".
Latvian Prime Minister Andris Kulbergs, in a post on X, hailed "swift decision-making and professional action" over the incident.
A French army spokesperson confirmed French warplanes had shot down an unidentified drone and a NATO official said: "It shows once again NATO's determination and ability to deter and defend."
The final decision to shoot down the drone was taken by NATO command, Latvian defence minister Raivis Melnis told reporters.
Latvia said Russia had been identified as using electronic warfare before the drone entered the country and was shot down on Monday morning near the village of Berzgale about 30km from the border.
No one was hurt and no property was damaged, Melnis said.
Authorities had earlier warned people in eastern Latvian regions to shelter indoors because of the threat.
NATO and EU member Latvia, which borders both Russia and Belarus, has seen a rising number of drone incidents in recent months.
On several occasions, stray drones used by Ukraine to strike targets in northwestern Russia have ended up in Latvia's airspace and crashed.
So far, no significant damage or loss of life has been caused.
However, the incidents triggered a political crisis in Latvia and led to a change of government.
Numerous military vehicles were seen driving along the rural roads around Berzekne and surrounding villages on Monday afternoon looking for drone debris in high grass.
Military drones straying into the airspace of Russia's neighbours have stoked concerns that Russia's war in Ukraine is spilling over NATO's borders.
Fragments of a Ukrainian drone were found in a field in Moldova on Monday after it entered from Ukraine - an incident that Moldovan officials blamed on Russia because of its war with Ukraine.
Estonian Foreign Minister Margus Tsahkna said the incidents in Latvia and Moldova "confirm that Russia's continued aggression against Ukraine poses a threat beyond Ukraine's borders".
An army official told Reuters in May that Latvia was increasing anti-drone defences.
Ukraine has stepped up long-range drone attacks on Russia, including in the Baltic Sea area, where several Ukrainian military drones have strayed into the airspace of Finland, Latvia, Lithuania and Estonia.
Ukraine blamed the incidents on Russia affecting the drone paths with electromagnetic warfare.
The French army jet that shot down the drone on Monday is part of the NATO Baltic Air Police mission, which has patrolled the skies of Latvia, Lithuania and Estonia since they joined the NATO military alliance in 2004.
The three Baltic countries do not have their own fighter jets.
The mission also currently includes Romanian F-16 fighters and Portuguese F-16 fighters.
Last month a Romanian military jet on the Baltic Air Police mission shot down a suspected Ukrainian drone over Estonia.
with DPA
