The response came despite an assurance from Condoleezza Rice, the US secretary of state, that Russia had nothing to fear from the missile pact.
She also denied the possibility of a new Cold War.
"Missile defence of course is aimed at no one. It is in our defence that we do this," said Rice, adding later: "It is not aimed in any way at Russia."
The US plans to base 10 interceptor missiles in Poland and a radar facility in the neighbouring Czech Republic between 2011 and 2013.
Washington says the missile system is aimed at protecting it and Europe from possible future attacks from "rogue states" such as Iran.
"Such a battery can have nothing to do with parrying imaginary Ianian threats"
Russian foreign ministry
But Russia says Washington and Warsaw rushed into finalising the deal as a response to its own military moves in Georgia.
Al Jazeera's Neave Barker, reporting from Moscow, said Russia saw the missile system as a threat to itself rather than a shield against "rogue states" as the US insists.
Our correspondent explained that from the Russian perspective, Poland was using the recent conflict between Georgia and Russia as a pretext to support its own domestic issues, its own desires and its own defences.
Russia took particular exception to a US agreement to deploy an additional battery of Patriot air-defence missiles in Poland starting next year as part of the broader shield deal.
"Such a battery can have nothing to do with parrying imaginary Iranian threats," Russia's foreign ministry said on Wednesday.
Warsaw's demands that the US bolster Polish security with Patriot missiles in exchange for hosting the broader interceptor missile base stalled the 18-month talks recently, but Washington agreed to do so last week, as Poland invoked the Georgia conflict to strengthen its case.
The Patriots are meant to protect Poland from short-range missiles from neighbours - such as Russia.
Lech Kaczynski, the Polish president, said the shield was purely defensive.
"For that reason, no one who has good intentions toward us and toward the Western world should be afraid of it," he said.
But some Russian politicians and generals have warned Poland of severe punishment.
"Poland, by deploying [the system] is exposing itself to a strike - 100 per cent," General Anatoly Nogovitsyn was reported as saying last week by the Interfax news agency.
Nato on Tuesday denounced threats against alliance member Poland as "unacceptable".
It endorsed the missile plan for Europe at its summit in Bucharest in April even though some allies were sceptical about its effectiveness and concerned it could lead to a new arms race.
The missile pact is bound to worsen an already tense standoff between Russia and Nato.
On Tuesday, Nato said there could be no business as usual with Russia and threatened to halt co-operation with Moscow unless Russia pulled back its troops to pre-conflict positions in Georgia.
On Wednesday, Russia went ahead and announced plans to cut military ties with the alliance, according to Norway.
Norway's defence ministry on Wednesday said "a well-placed official in the Russian ministry of defence" had called to inform about plans to freeze all military ties with the Western alliance.
Espen Barth Eide, the state secretary at the ministry, said the official who telephoned its embassy in Moscow said a written note on the plan would be sent soon.
Under a 2002 agreement that set up the council, the former Cold War foes began co-operating in counterterrorism patrols, enforcement work and developing battlefield anti-missile technology.