Polish Prime Minister Donald Tusk said operations were ongoing and that he was in "constant contact" with NATO Secretary General Mark Rutte.
Tusk has called for an emergency meeting of the council of ministers at 8am (4pm AEST) on Wednesday, a government spokesman said.
Poland's military command said drones repeatedly violated Polish airspace during the Russian attack across the border, in western Ukraine.
Radars tracked more than 10 objects and those that could pose a threat were "neutralised," the command said.
"Some of the drones that entered our airspace were shot down. Searches and efforts to locate the potential crash sites of these objects are ongoing," it said in a statement.
It urged people to stay at home, naming the regions of Podlaskie, Mazowieckie, and Lublin as most at risk, adding: "This is an act of aggression that posed a real threat to the safety of our citizens."
Russia's defence ministry did not immediately respond to a Reuters request for comment.
US Secretary of State Marco Rubio had been briefed, CNN reporter Kaitlan Collins said on Tuesday. The State Department did not immediately respond to a request for comment.
Chopin airport in Warsaw, the country's largest, announced that its airspace was closed due to military actions.
Flightradar24 tracking data showed a number of flights due to land early on Wednesday morning at Chopin were diverting to airports in Poland's Katowice, Wroclaw and Poznan.
The US Federal Aviation Administration earlier said Chopin was one of four Polish airports to be temporarily closed, including Rzeszow–Jasionka Airport in the southeast, a hub for passenger and arms transfers to Ukraine.
Most of Ukraine, including western regions of Volyn and Lviv which border Poland, had been under air raid alerts for nearly all night, according to Ukraine's air force.
Earlier, Ukraine's air force reported that Russian drones had entered NATO-member Poland's airspace, posing a threat to the city of Zamosc.
US Democratic Senator Dick Durbin said repeated violations of NATO airspace by Russian drones were a sign that Russian President "Vladimir Putin is testing our resolve to protect Poland and the Baltic nations".
"After the carnage Putin continues to visit on Ukraine, these incursions cannot be ignored," he said on X.
Republican representative Joe Wilson, a senior member of the Foreign Affairs Committee, said in a post on X that Russia was "attacking NATO ally Poland" with drones, calling it an "act of war".
Wilson urged US President Donald Trump to respond with sanctions "that will bankrupt the Russian war machine".
"Putin is no longer content just losing in Ukraine while bombing mothers and babies, he is now directly testing our resolve in NATO territory," he said.
Trump, who warmly welcomed Putin to the United States for a summit in August, said over the weekend he was ready to move to a second phase of sanctioning Russia after months of fruitless talks about a peace deal.
It was his strongest indication yet that he may escalate pressure on Moscow or its oil buyers in response to the war in Ukraine.
