The clip, posted on militant websites associated with the extremist group, featured the British-accented militant widely known as "Jihadi John" who appeared in the beheading videos of four Western hostages last year.
Yukawa is a 42-year-old widower who reportedly has a history of attempted suicide and self-mutilation after his military goods business went bankrupt and his wife died of cancer.
He even considered cutting off his genitals because of his perceived failures in life, deciding that he would instead "live as a woman and leave the rest to destiny".
He travelled to Iraq and Syria last year after telling friends and family that he thought it represented a last chance to turn his life around.
Pictures on his Facebook page show him in Iraq and Syria in July.
One video on his page showed him test-firing a Kalashnikov assault rifle with the caption: "Syria war in Aleppo 2014."
In his last blog post, he says: "I cannot identify the destination. But the next one could be the most dangerous."
He added: "I hope to film my fighting scenes during an upcoming visit."
He came to widespread attention in Japan when he appeared in footage posted last August in which he was shown being roughly interrogated by his captors.
Yukawa's father, Shoichi Yukawa, has declined to comment, saying he was overwhelmed by the news reports of capture by ISIS.
Goto is a freelance journalist, born in 1967, who set up a video production company, named Independent Press in Tokyo in 1996, feeding video documentaries on the Middle East and other regions to Japanese television networks, including public broadcaster NHK.
He had been out of contact since late October after telling family that he intended to return to Japan, NHK reported.
Goto met Yukawa last year and helped him travel to Iraq in June, he told Reuters in August.
Footage on his last Twitter post in October shows him talking in front of the Syrian city of Kobani, which has been under siege from ISIS fighters for several months.
In early November, his wife received e-mail demands for about one billion yen in ransom from a person claiming to be an Islamic State group member, Fuji TV said.
The emailed threats were later confirmed to have come from a sender implicated in the killing of US journalist Foley, Fuji TV said.
In the latest ISIS video, the militant directly addresses Japanese Prime Minister Shinzo Abe, who is currently now on a six-day visit to the Middle East.
Brandishing a knife and dressed all in black, he says: "To the prime minister of Japan: Although you are more than 8000 and 500 kilometres from the Islamic State, you willingly have volunteered to take part in this crusade.
"You have proudly donated US$100 million to kill our women and children - to destroy the homes of the Muslims. So the life of this (points knife at Kenji Goto Jogo) Japanese citizen will cost you US$100 million.
"And in an attempt to stop the expansion of the Islamic State, you also donated another US$100 million to train the mujahideen against the mujahideen. And so the life of this (points knife at Haruna Yukawa) Japanese citizen will cost you another US$100 million.
"And to the Japanese public: Just as your government has made the foolish decision to pay US$200 million to fight the Islamic State, you now have 72 hours to pressure your government into making a wise decision by paying the US$200 million to save the lives of your citizens. Otherwise, this knife will become your nightmare."
Mr Abe said Japan would not bow to 'terrorism' and pledged to honour his promise of aid.
"I strongly demand that they not be harmed and that they be immediately released," he told a news conference in Jerusalem. "The international community will not give in to terrorism and we have to make sure that we work together."
- Daily Mail
