He died when a group of men threw a grenade at his vehicle and fired automatic weapons, the source said on Wednesday.
"He was on his way to Baghdad with a security escort of four cars, when the attackers in another car pulled up beside his vehicle and threw a grenade, and then shot at his car," said the source, who declined to be named.
A spokesman for the governorate has confirmed that the governor of Mosul, Usama Kachmula, and two people who were accompanying him were killed.
"The governor was killed in the region of T'lul al-Baj, 110km south of Mosul, with two people who were with him," said the spokesman, Hazam Jalawi, without explaining how they died.
Several senior officials working for the interim Iraqi government, which took power from the US-led occupying coalition barely two weeks ago, have been assassinated recently.
A series of explosions left 44
people killed in Mosul last month
Earlier, unknown armed men also shot dead a senior official from Iraqi's industry ministry as he left his home in Baghdad to go to work, said an interior ministry spokesman.
The attack on Sabir Karim, a director general at the ministry, took place on Tuesday morning, said Colonel Adnan Abd al-Rhaman, adding that the assailants then fled the scene.
'Al-Qaida' suspects detained
In the southern Iraqi city of Najaf a group suspected of having ties to al-Qaida were arrested, reported Aljazeera.
Colonel Ghalib al-Jazairy, Najaf's police commissioner, was quoted as saying that the group was involved in last year's assassination of Muhammad Baqir al-Hakim, the head of the Supreme Council for the Islamic Revolution.
They are also accused of carrying out a string of attacks in Karbala last year.