The footage issued yesterday shows a masked militant, believed to be the Briton known as Jihadi John, making the threat.
It comes three days after Japanese Prime Minister Shinzo Abe pledged the same sum in non-military assistance for countries battling IS in Iraq and Syria.
In the video, the speaker says the two hostages are under threat as a result of Japan’s support of Western military actions against IS.
Brandishing a knife and dressed all in black, the militant says: “To the prime minister of Japan: Although you are more than 8,000 and 500 kilometres (5,280 miles) from the Islamic State, you willingly have volunteered to take part in this crusade.
“You have proudly donated $100m (£66m) to kill our women and children, to destroy the homes of the Muslims, so the life of this Japanese citizen will cost you $100m.
“And in an attempt to stop the expansion of the Islamic State, you have also donated another $100m to train the murtadeen (apostates) against the mujahideen, and so the life of this Japanese citizen will cost you another $10m.
“And to the Japanese public: Just as how your government has made the foolish decision to pay $200m to fight the Islamic State, you now have 72 hours to pressure your government in making a wise decision, by paying the $200m to save the lives of your citizens.
“Otherwise, this knife will become your nightmare.”
The hostages – identified as Kenji Goto Jogo and Haruna Yukawa – appear in the same orange jumpsuits as those worn by captives in previous IS videos.
The clip is filmed in a desert location.
Japanese Prime Minister Shinzo Abe described the threat as “unforgiveable” and demanded that IS immediately release the men.
He added: “I feel strong resentment.”
The Foreign Office confirmed it was aware of the video and is “studying the content”.
Jihadi John has appeared in a number of previous videos in which hostages were both threatened and killed.
British aid workers David Haines, who was born in Holderness in East Yorkshire, and Alan Henning and US journalists Steven Sotloff and James Foley have been beheaded in similar style footage.
British photojournalist John Cantlie has appeared in a number of propaganda videos released by “Islamic State”, presenting documentary-style clips.
The latest video is thought to be the first time the group has made a specific demand for cash for hostages.
Downing Street confirmed that UK security agencies were analysing the video.