A statement by the ministry on Monday said medical checks on a man in custody showed he was not Izzat Ibrahim al-Duri, who was vice president of Iraq and deputy chairman of the Revolutionary Command Council.
"The person that has been arrested, after appropriate medical tests, was not al-Duri but somebody related to him, who is also wanted by the state," the ministry said.
The announcement followed 24 hours of confusion during which several officials said al-Duri had been captured.
The confusion deepened on Monday morning after an Iraqi health ministry official denied a suspect was undergoing DNA tests.
Al-Duri was reportedly captured in Tikrit on Sunday and the interim Iraqi prime minister's office said tests were being carried to check his identity.
Initially, officials provided details about the fighting which erupted on Saturday between the Iraqi national guard and resistance fighters trying to prevent al-Duri's arrest in his native village of al-Dawr that reportedly left 70 killed or wounded.
However, the Health Ministry official said there was no report of any dead or wounded for Saturday in Salah al-Din province, which includes al-Dawr.
Al-Duri has been a staunch ally of
Saddam since the 1960s
"There was no operation to arrest Izzat al-Duri in my province and I have no idea where all this false and irresponsible information came from," Salah al-Din governor Hamad Hamud al-Qaisi said.
"There were searches in the past few days and this is all we know."
The national guard commander in the nearby city of Tikrit, Colonel Abd Allah al-Juburi, was one of the officials who broke the news of al-Duri's capture on Sunday, boasting the achievement of his troops.
But on Monday, he backtracked and said: "This is a purely American operation and they told me about it on Saturday. We have nothing to do with this story."
"There was no operation to arrest Izzat al-Duri in my province and I have no idea where all this false and irresponsible information came from"
Hamad Hamud al-Qaisi,
Salah al-Din province governor
Al-Duri was one of the former Iraqi government's better known figures, and was frequently sent abroad to represent his country's interests.
On the run, he is accused by US occupation forces of being one of the key leaders of the Iraqi resistance.
However, reports have suggested al-Duri is suffering from leukaemia.