“Drones are an effective way to deliver two or three kilogrammes (one or two pounds) of TNT, land them on a target and detonate them,” former anti-terror officer Alexei Filatov told RBK.
Russia has set up dozens of no-flight zones and other air space restrictions for the coming months.
These cover not only the stadiums and 11 host cities but also training grounds and hotels that will be used by the 32 participating national teams.
The transportation ministry has identified 41 locations around which all types of flights – from drones to planes – are prohibited.
These stretch from anywhere between 500m (500 yards) and 10m (six miles).
But operating a drone will be illegal within around 100km of any of the 11 host cities.
Drone flights over Moscow are permanently banned.
Russian state media have been issuing regular reporters in recent months of state security services conducting raids that led to the capture of alleged terror masterminds.
President Vladimir Putin also took the unusual step in December of personally thanking US counterpart Donald Trump for providing intelligence that helped avert the bombing of a major cathedral in Saint Petersburg.