It also appealed to Mr Goto's wife and his colleagues at Independent Press to pressure the Japanese Prime Minister Shinzo Abe for his release.
The images and audio have not been verified and vary greatly from previous videos released by the group.
The Japanese Government said it is trying to verify the reports. Chief cabinet secretary Yoshihide Suga said cabinet ministers were holding an emergency meeting about the new message.
Prime Minister Abe told reporters after the news broke: "This is an outrageous and unacceptable act of violence.
"We strongly demand the prompt release of the remaining captive Kenji Goto, without harm."
"We will not give in to terrorism," he later said.
A foreign correspondent for The New York Times said on Twitter: "Isis source has sent me audio allegedly of Kenji Goto stating that Haruna has been beheaded.
"Isis has now dropped ransom demand and is asking for a prisoner exchange for a 'sister' detained in Jordan."
It comes after a 72-hour deadline for a US$200 million ransom was delivered in a video on Tuesday. The militant in that video had threatened to kill both men if the Japanese Government did not pay $100m for each hostage.
On Friday, Mr Goto's mother Junko Ishido issued an emotional plea to spare the life of her son, telling militants: "My son is not an enemy of the Islamic State."
Ms Ishido told a news conference her son's wife had recently given birth and implored militants to release him, saying the child needed a father.
Mr Yukawa, who describes himself as having his own 'private military company' on his Facebook, is believed to have been captured by Isis militants near Aleppo in August after travelling to Syria.
Mr Goto, a seasoned war correspondent who had reported in the Middle East previously, also travelled back to the region later in the year. The last correspondence from him was received by his family in October after he crossed the border into Syria from Istanbul.
Mr Goto had reportedly gone to Syria to help secure Mr Yukawa's release after seeing video footage of his capture.
- The Independent