There is also the potential risk of a cyberattack on Ukraine's air traffic control.
Ukraine has closed its airspace to civilian flights from today, citing a high risk to safety.
Europe's aviation regulator has also warned against the hazards of flying in bordering areas of Russia and Belarus, due to military activities.
Russian President Vladimir Putin has authorised a military operation in eastern Ukraine in what appears to be the start of a war in Europe.
On its website, Ukraine State Air Traffic Services Enterprise said the country's airspace was closed to civilian flights starting from 0045 GMT on Thursday, with air traffic services suspended.
The European Union Aviation Safety Agency (EASA) said airspace in Russia and Belarus within 100 nautical miles of their borders with Ukraine could also pose safety risks.
"In particular, there is a risk of both intentional targeting and misidentification of civil aircraft," the agency said in a conflict zone bulletin.
"The presence and possible use of a wide range of ground and airborne warfare systems poses a high risk for civil flights operating at all altitudes and flight levels."
The aviation industry has taken heightened notice of the risks conflicts pose to civil aviation since Malaysia Airlines flight MH17 was shot down over eastern Ukraine in 2014.
EASA said Russia's defence ministry had sent Ukraine an urgent message warning of a high risk to flight safety, due to the use of weapons and military equipment - and asked Ukraine's air traffic control to stop flights.
Ukraine has been declared a conflict zone
Websites which had shown intelligence-gathering flights over or near Ukraine, as the West deliberately showcased support by transmitting detectable signals in recent weeks, showed empty space as aircraft left and Ukraine was declared a conflict zone.
Early morning airline traffic skirted the whole country in crowded corridors to the north and west.
An El Al flight from Tel Aviv to Toronto made a sudden U-turn out of Ukraine's airspace around the time of its closure, flight tracking website FlightRadar24 showed.
A LOT Polish Airlines flight from Warsaw to Kyiv also turned back to Warsaw around the same time.
Hours earlier, Safe Airspace, which was set up to provide safety and conflict zone information after the downing of MH17, said it had increased its risk level over Ukraine to "do not fly".
It also warned of the potential for a cyberattack on Ukraine's air traffic control.
Russia said on Thursday it had suspended domestic flights to and from several airports near its border with Ukraine, including Rostov-on-Don, Krasnodar and Stavropol, until March 2.
Russia has also closed some airspace in the Rostov sector "in order to provide safety" for civil aviation flights, a notice to airmen showed.
Before Ukraine advised of the airspace curbs, Britain, Canada, France, Italy and the United States had told their airlines to avoid certain airspace above eastern Ukraine and Crimea, but stopped short of a total ban.
Germany's Lufthansa halted flights to Ukraine from Monday, joining KLM which had already suspended flights.
Last week, two Ukrainian airlines disclosed problems in securing insurance for some flights while foreign carriers began avoiding the country's airspace as Russia massed a huge military force on its border.