The test launch, which also included the firing of several other missiles, comes amid growing tensions over Iran's nuclear programme, which the West fears could be aimed at making an atomic bomb.
The US condemned the tests and said Tehran should refrain from such exercises.
"The aim of these war games is to show we are ready to defend the integrity of the Iranian nation," Al-Alam quoted Hossein Salami, the Revolutionary Guards air force commander, as saying.
"Our missiles are ready for shooting at any place and any time, quickly and with accuracy.
"The enemy must not repeat its mistakes. The enemy targets are under surveillance," he added.
Desert location
In total nine missiles were tested, state-run English language channel Press-TV reported.
Along with the Shahab-3, the missiles tested were the Zelzal, which has a range of up to 400km, and the Fateh, which has a range of around 170km.
Press-TV showed pictures of the Shahab-3 being launched at an undisclosed desert location inside Iran.
"This a show of Iran's military muscle in the region in the face of threats from countries who said they would target Iran's nuclear facilities," the Press-TV announcer said.
Significantly, an aide to Ayatollah Ali Khamenei, Iran's supreme leader, said on Tuesday that Iran would "set fire" to Israel and the US navy in the Gulf as its first response to any American attack over its nuclear programme.
"The first US shot on Iran would set the United States' vital interests in the world on fire," Ali Shirazi, a mid-ranking cleric who is Khamenei's representative to the naval forces of the Revolutionary Guards, said.
US report
The test launch came on the same day that a US foreign affairs commitee began delivering its report on the state of relations between the US and Iran.
William Burns, under-secretary of state for political affairs, said Iran should move towards a "co-operative and constructive" path.
"Until that time, however, the US and the international community remain committed to meeting the challenges posed by Iran," he told the congressional hearing.
Burns called for "tough minded diplomacy, maximising pressure on the Iranians at multiple points to drive home the costs of continued defiance of the rest of the world, especially on the nuclear issue".
But he said that while Iran had sought to "create a perception of advancement" on its nuclear programme, "real progress has been more modest".
"It is apparent that Iran has not yet perfected enrichment, and as a direct result of UN sanctions, Iran's ablity to procure technology or items of significance to its missile programmes, even dual-use items, is being impaired," he said.
'Threat of force'
Michael Williams, head of the transatlantic programme at the Royal United Services Institute in London, told Al Jazeera: "Diplomacy is being backed by the threat of a military strike at some point; it remains on the table.
The [US] is certainly working with the international community to push forward additional sanctions and that is something that the US president has been trying to do for some time now.
"It looks now like they are going to target some more specific institutions in Iran. The sanctions have also been so broad in the sense that they are affect businesses that want to do business with Iran - so essentially if you do business there you cannot do business in America, which is a de facto global sanction.
"Quite frankly, there is a palpable fear in Europe about the Iranian nuclear programme; one, they are very concerned about the implications of Iran developing a nuclear weapon ... and secondly they are worried that the Israelis are seeing a window closing and that there may be strikes against Iran that would then cause things to spiral out of control."
West critical
Reaction to the news of the Iranian test launch from the US and its allies was uniformly critical.
"Iran's development of ballistic missiles is a violation of United Nations Security Council resolutions and completely inconsistent with Iran's obligations to the world," Gordon Johndroe, the White House spokesman, said.
He expressed concern that Iran's ballistic missiles could be used as "a delivery vehicle for a potential nuclear weapon".
The British foreign office described the tests as "unwelcome".
Eric Chevallier, a French foreign ministry spokesman, said: "These missile tests can only reinforce the concerns of the international community at a time when Iran is separately developing a nuclear programme."
A German government spokesman, Thomas Steg, said: "We call on Iran to refrain from any kind of sabre-rattling."
In Israel, a spokesman for Ehud Olmert, the prime minister, said Israel is not seeking war.
Mark Regev said: "Israel seeks neither conflict nor hostilities with Iran, but no one in the international community should remain indifferent to Iran's nuclear programme and Iran's ballistic missile programme."