He did not say whether the short-range Iskander missiles would be fitted with nuclear warheads.
In his first state of the nation speech, President Medvedev also blamed the US for the war in Georgia and the global financial crisis.
He said he hoped Barack Obama would act to improve relations with Russia but he did not offer congratulations to the president-elect.
President Medvedev also proposed increasing the Russian presidential term to six years from the current four, a major constitutional change that would further increase the power of the head of state and could deepen Western concern over democracy in Russia.
The president said the Iskander missiles will be deployed to Russia's Kaliningrad region, which lies between Poland and the ex-Soviet republic of Lithuania on the Baltic Sea, but did not say how many would be used.
Equipment to electronically hamper the operation of prospective US missile defence facilities in Poland and the Czech Republic will be deployed, he said.
President Medvedev singled out the United States for criticism, casting Russia's war with Georgia in August and the global financial turmoil as consequences of aggressive, selfish US policies.
"Mechanisms must be created to block mistaken, egotistical and sometimes simply dangerous decisions of certain members of the international community," he said shortly after starting the 85-minute speech.
President Medvedev, whose criticism of Washington echoed addresses by his predecessor Vladimir Putin, made it clear he was referring to the US
The president said Georgia sparked the August war on its territory with what he called "barbaric aggression" against Russian-backed South Ossetia.
The conflict "was, among other things, the result of the arrogant course of the American administration, which did not tolerate criticism and preferred unilateral decisions."
President Medvedev also painted Russia as a country threatened by growing Western military might.
"From what we have seen in recent years, the creation of a missile defence system, the encirclement of Russia with military bases, the relentless expansion of Nato, we have gotten the clear impression that they are testing our strength," President Medvedev said.
He announced deployment of the short-range missiles as a military response to US plans to deploy missile-defence facilities in Poland and the Czech Republic - former Soviet satellites that are now Nato members.
Speaking just hours after Mr Obama was declared the victor in the US presidential election, President Medvedev said he hoped the incoming administration will take steps to improve badly damaged US ties with Russia.
He suggested it is up to the US - not the Kremlin - to seek to improve relations.
"I stress that we have no problem with the American people, no inborn anti-Americanism. And we hope that our partners, the US administration, will make a choice in favour of full-fledged relations with Russia," President Medvedev said.
Tension in Russian-American relations has been driven to a post-Cold War high by Moscow's war with US ally Georgia.
On the financial crisis, President Medvedev said overconfidence in American dominance after the collapse of the Soviet Union "led the US authorities to major mistakes in the economic sphere."
The administration ignored warnings and harmed itself and others by "blowing up a money bubble to stimulate its own growth," he said.
President Medvedev said the president's tenure should be lengthened to six years to enable the government to more effectively implement reforms.
He said the term of the parliament also should be extended by a year to five years, and that parliament's power must be increased by requiring the Cabinet to report to MPs regularly.
The proposals were President Medvedev's first major initiative to amend the constitution since he was elected in March to succeed his long-time mentor Putin.
Mr Putin, who is now prime minister and has not ruled out a return to the Kremlin in the future, has said that the presidential term should be increased.
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