Jebbar Jabr Solagh was abducted at 7.30pm (1530 GMT) as he drove home to the capital's district of Sadr City, where he also works as a hospital director, Major Felah Al-Mohammedawi, a ministry spokesman said.
Solagh is the brother of Interior Minister Bayan Jabr Solagh, the head of Iraq's police forces.
"I didn't hear about it, and I have no information," Jabr, the minister, told reporters in Amman as he emerged from a meeting with his Jordanian counterpart.
An hour before Solagh was abducted, armed men in the town of Taji, north of Baghdad, kidnapped Firas Marid, the son of a brigadier-general who heads the office of tribal affairs in the interior ministry, al-Mohammedawi said.
The abduction comes amid a wave of violence which has gripped the capital ahead of the 15 October national referendum on Iraq's new constitution.
Earlier in an exclusive interview with Aljazeera, Minister Solagh said the Iraqi government had obtained documents indicating that the al-Qaida network was considering leaving Iraq.
Solagh said a letter written by Abu Azzam to al-Zarqawi, obtained during the recent Tal Afar operation, showed al-Qaida was contemplating moving to neighbouring countries.