The military facility at Simferopol was stormed by gunmen who opened fire with automatic weapons. The dead soldier had been manning a guard tower and one of the injured was a captain, according to reports.
The Ukrainian defence ministry claimed the attackers had been wearing Russian military uniforms and were holding the base commander in a nearby building last night.
Until now forces deployed on the Black Sea peninsula – taken over three weeks ago by Russian forces – had been told to avoid using arms against attack.
It came shortly after Vladimir Putin and the leaders of Crimea signed a bill to formally absorb the peninsula into Russia.
In an anger-tinged speech, the Russian president claimed the West was supporting a new “extremist” right-wing government in Ukraine, despite the pro-EU administration being widely seen as moderate.
The development came as the United States confirmed it is considering sending troops for war games in the Baltic states bordering Russia. Vice president Joe Biden said the move would be to reassure Nato allies in Europe alarmed at the Kremlin’s intervention in Ukraine.
Moscow’s despatch of troops to Crimea and its unilateral declaration the area is now part of Russia that have left Nato member states in eastern Europe worried they could be next in line.
In the Polish capital on the first leg of a two-day trip to the region, Mr Biden condemned Russia’s actions as a land grab, and he said Nato’s commitment to protect any of its members from attack was unwavering.
He also said the US would work on reducing the dependence of eastern European states on imported Russian fuel, a relationship that, US officials say, the Kremlin uses as a tool of political influence.
Mr Biden’s suggestion of sending US troops for military exercises in the Baltics, if implemented, would represent the strongest evidence to date of Washington’s resolve in backing up its Nato allies on Russia’s doorstep.
The three Baltic states – Estonia, Latvia and Lithuania – are in Nato and the European Union. Yet they are particularly vulnerable to any Russian action, being small, having sizeable Russian-speaking minorities, and they depend on Russia for energy and trade. The developments came after Mr Putin defied Western anger by announcing new laws allowing Crimea to join the Russian Federation.
Prime Minister David Cameron accused Moscow of a “flagrant breach of international law”, trying to annex the region on the basis “of a sham referendum held at the barrel of a Russian gun”.
He added: “President Putin should be in no doubt that Russia will face more serious consequences and I will push European leaders to agree further EU measures when we meet on Thursday.”
Downing Street was already pushing for further EU sanctions, which would be discussed in detail by the 28 nations at the European Council in Brussels.
Britain is backing a call by US president Barack Obama for the G7 nations – the US, UK, Germany, France, Italy, Japan and Canada – and the EU to discuss the crisis at a security summit in the Netherlands next Monday.
During a speech at the Kremlin, Mr Putin accused the West of behaving “irresponsibly” in backing an “extremist” uprising to oust pro-Moscow president Viktor Yanukovych in Kiev.
He said: “In the hearts and minds of people, Crimea has always been, and remains, an inseparable part of Russia.”
The result of Sunday’s referendum, which produced a 96 per cent majority in favour of leaving Ukraine, was “more than convincing”, he said.
He added: “The people of Crimea clearly and convincingly expressed their will – they want to be with Russia.”
Britain has suspended military co-operation and arms exports to Russia.
Mr Cameron said: “The steps taken by president Putin today to attempt to annex Crimea to Russia are in flagrant breach of international law and send a chilling message across the continent of Europe.
“The choice remains for president Putin: take the path of de-escalation or face increasing isolation and tighter sanctions.”