The incident marks the first time the alliance has downed an unmanned aircraft over the country.
It occurred at around 10:05 local time near a village roughly 30km from the Russian border.
No casualties or damage were reported.
Latvia's defence minister, Colonel Raivis Melnis, said it was not yet possible to determine where the drone was launched from or what type of aircraft it was.
The military said "Russian electromagnetic warfare" activity was detected shortly before the drone crossed into Latvian airspace.
France confirmed that one of its fighter jets taking part in NATO's Baltic Air Policing mission fired the shot.
The aircraft had taken off from a base in Lithuania.
Latvia's foreign minister said the incident showed NATO's determination to defend its member states.
He added that recent drone incidents in Romania and Latvia demonstrated that Russia's war in Ukraine posed risks beyond Ukrainian borders.
The Baltic states – Latvia, Lithuania and Estonia – do not operate their own combat aircraft.
Their airspace is instead protected by allied jets rotating through the Baltic Air Policing mission, which has run continuously since 2004.
The incident comes after a drone was shot down over Estonia on 19 May.
Also, last month, two Ukrainian drones targeting Russian territory fell on Latvian soil, damaging an oil storage facility in the city of Rēzekne.
(ał)
Source: PAP, Reuters