Their words: the measures are preventive, meant to secure and protect airspace near threatened regions.
We don't know how long this lasts yet, or how many flights are affected. That's everything we know.
Why this mattersSo is this new? Not really.
These two airports have shut down again and again this month. On 16 and 17 September, Polish fighter jets went up and air raid sirens sounded in both cities. That was after a Russian strike drone came down about 4 kilometres from the Polish-Ukrainian border.
More closures came around 13 September, 21 September and 23 September.
So this isn't a one-off. It's a near-weekly pattern.
And here's why Rzeszów matters so much. It sits right by Poland's border with Ukraine, one of the most watched stretches of NATO territory since Russia's full-scale invasion started, now more than four and a half years ago.
And Russia isn't easing off Kyiv either.
Overnight, ballistic missiles hit Ukraine's capital. More than a dozen explosions went off just before 3am local time. Parts of the city lost power.
Vitali Klitschko, Kyiv's mayor, says at least two people were hurt in the city itself.
In Vyshhorod, just outside Kyiv, a child was found dead under the rubble of a home. A man and a woman were also injured.
In Bucha, 11 vehicles, two warehouses and three homes were damaged.
So why should Poland be worried about a strike on Kyiv? Because its own Prime Minister, Donald Tusk, has been warning for weeks that Russia's plans go further than Ukraine.
Tusk says intelligence suggests Russia is planning hybrid drone and missile strikes against countries that support Ukraine. Poland is one of them.
That warning came days after a Russian drone hit a passenger train in Ukraine just two kilometres from the Polish border.
Poland's military hasn't said what threat triggered today's closures, or how long they'll last. Russia's military hasn't said anything at all.
So the question is the same one Poland keeps facing. Is this just routine caution about a war next door? Or is the war creeping closer to NATO territory itself?
Right now, Rzeszów and Lublin sit closed. And Kyiv is counting the damage from another overnight attack.