Nato has previously said implementing a no-fly zone could lead to widespread war in Europe against nuclear-armed Russia
Speaking at a meeting with female pilots on Saturday, Mr Putin said Russia would view "any move in this direction" as an intervention that "will pose a threat to our service members".
"That very second, we will view them as participants of the military conflict, and it would not matter what members they are," he said.
Ukrainian president Volodymyr Zelensky has pushed Nato to impose a no-fly zone over his country, warning that "all the people who die from this day forward will also die because of you", as Russian forces were battering strategic locations in Ukraine.
Nato has said a no-fly zone, which would bar all unauthorised aircraft from flying over Ukraine, could provoke widespread war in Europe with nuclear-armed Russia.
His comments came as a ceasefire to evacuate residents from two cities in Ukraine quickly fell apart, with officials saying work to remove civilians had halted amid shelling hours after Russia announced the deal.
The Russian defence ministry said early on Saturday that it had agreed on evacuation routes with Ukrainian forces for Mariupol, a strategic port in the south-east, and the eastern city of Volnovakha.
The vaguely worded statement did not make clear how long the routes would remain open.
But a short time later, Mr Zelensky's office said the ceasefire had already failed.
Deputy head of his office Kyrylo Tymoshenko said: "The Russian side is not holding to the ceasefire and has continued firing on Mariupol itself and on its surrounding area.
"Talks with the Russian Federation are ongoing regarding setting up a ceasefire and ensuring a safe humanitarian corridor."
Russia breached the deal in Volnovakha as well, deputy prime minister Iryna Vereshchuk told reporters.
"We appeal to the Russian side to stop firing," she said.
Russian outlet RIA Novosti carried a Russian defence ministry claim that the firing came from inside both communities against Russian positions.
The struggle to enforce the ceasefire shows the fragility of efforts to stop fighting across Ukraine as people continue to flee the country by the thousands.
Mr Zelensky said: "We are doing everything on our part to make the agreement work. This is one of the main tasks for today. Let's see if we can go further in the negotiation process."
Mariupol had become the scene of growing misery amid days of shelling that knocked out power and most phone service and raised the prospect of food and water shortages for hundreds of thousands of people in freezing weather.
Pharmacies are out of medicine, Doctors Without Borders said.
The head of Ukraine's security council, Oleksiy Danilov, had urged Russia to create humanitarian corridors to allow children, women and the older adults to flee the fighting, calling them "question number one".
Meanwhile, diplomatic efforts continue as US secretary of state Antony Blinken arrived in Poland to meet the prime minister and foreign minister, a day after attending a Nato meeting in Brussels in which the alliance pledged to step up support for eastern flank members.
Aeroflot, Russia's flagship state-owned airline, announced that it plans to halt all international flights, except to Belarus, starting on Tuesday in the wake of Western sanctions imposed on Russia.
The country's aviation agency, Rosaviatsiya, had recommended that all Russian airlines with foreign-leased planes halt passenger and cargo flights abroad to prevent the aircraft from being impounded.
But as the United States and other Nato members send weapons for Kyiv and more than one million refugees spill through the continent, the conflict is already drawing in countries far beyond Ukraine's borders.
Russia continues to crack down on independent media reporting on the war, also blocking Facebook and Twitter, and more outlets say they are pausing their work inside the country.
And in a warning of a hunger crisis yet to come, the UN World Food Programme says millions of people inside Ukraine, a major global wheat supplier, will need food aid "immediately".
Mr Zelensky was set to brief US senators Saturday by video conference as US congress considers a request for 10 billion dollars (£7.5 billion) in emergency funding for humanitarian aid and security needs.
In a video message to anti-war protesters in several European cities, Mr Zelensky appealed for help, warning: "If we fall, you will fall."