He said Russia controlled the Crimea, in violation of Ukraine’s sovereignty, and warned of “significant costs” if its troops did not withdraw.
He urged Ukraine and Russia to hold talks and suggested Russia’s membership of the G8 could be under threat,
Vladimir Putin has said Russia reserves the right to protect its interests
Ukraine has ordered a full military mobilisation in response to Russia’s build-up of forces on the Crimean peninsula, which was part of Russia until 1954.
No 10 has ruled out military intervention, saying the “only avenue that is being pursued is a diplomatic and peaceful one”.
Mr Hague, who travelled to Kiev on Sunday to meet the new Ukrainian government, told the BBC that Russia had “legitimate” interests in the region.
But he said its actions were unacceptable and required a “strong” response from the international community.
It is a very tense and dangerous situation that Russia’s intervention has now produced,” he told BBC Radio 4’s Today, adding that there was now a constant risk of a “flashpoint”.
“The world cannot just allow this to happen. The world cannot just say it is OK, in effect, to violate the sovereignty of another nation in this way.”
Mr Hague rejected claims the US and EU were powerless to act, saying they had a range of options at their disposal if Russian forces did not return to their naval bases in Crimea and honour the terms of an agreement with Ukraine allowing them to station forces there.
The UK has said Russia will face “significant costs” if it does not pull back, with economic action not being ruled out.
Speaking after meeting Ukraine’s interim president and prime minister, Mr Hague said Russia’s actions could not be allowed to become the “normal way to behave in international affairs”.
The foreign secretary said there was a “serious threat to G8 co-operation in the coming weeks and months”.
The UK and other G7 nations have already said they are suspending preparations for this year’s G8 summit in Russia, while the US has hinted at stronger measures, such as possible sanctions and asset freezes on Russian business.
The G7, which comprises the UK, US, Canada, France, Germany, Italy and Japan, has called on Moscow to “address any ongoing security or human rights concerns that it has with Ukraine through direct negotiations”.
It has also repeated its commitment to provide substantial financial backing to the new Ukrainian government, with talks with the International Monetary Fund due to begin in the coming days.
The UK is to give £10m to Kiev to support economic and political reforms.
In a separate development, Buckingham Palace said Prince Edward has cancelled a visit to the Sochi Paralympics.
A statement said: “The Earl of Wessex, patron of the British Paralympic Association has, on the advice of government, cancelled a planned visit to Russia between 11 and 14 March to attend the Sochi Paralympic Games.”
The UK government has also said no British ministers will attend the event although a spokesman said Mr Cameron remained “fully supportive of our Paralympic athletes’ participation at Sochi”
The Russian incursion was triggered by former Ukrainian leader Viktor Yanukovych’s removal from power following four months of street protests that culminated in bloody clashes between demonstrators and security forces.
The Foreign Office has advised against all travel to Crimea, and urged British nationals in the peninsula to leave.
It said it was not able to provide consular services to anyone choosing to remain in Crimea.