Al-Qaida ally Abu Musab al-Zarqawi's group had said in an internet video on Wednesday it would behead 24-year-old Koda within 48 hours if Japan did not withdraw its troops from Iraq.
Prime Minister Junichiro Koizumi, a close ally of US President George Bush, has said Japan's non-combat troops will stay in southern Iraq.
Takashima said Japan had been informed the body was found between Baghdad and the northern Iraqi city of Tikrit by the US military.
It was not clear exactly when al-Zarqawi group's deadline expired, but the media quoted Japanese officials as saying they believed it passed at 8pm (1700 GMT).
Members of Koda's family have begged for the life of the young man who they said had no ties to Japan's military, no political agenda and was not in search of personal gain.
Japan has 550 troops in Iraq
Tokyo has sought help over Koda from about 25 countries, including the United States, Britain and nations in the Middle East, and has sent a special envoy to Jordan.
Japan has about 550 troops at Samawa, 270km south of Baghdad.