A security operation is now under way in the city in an effort to find him.
Aden is the city closest to Yemen's Abyan province where government forces have been struggling to contain militant groups linked to al-Qaeda.
In the past year these groups have consolidated their control over several towns and villages in the region, including Abyan's capital Zinjibar.
Kidnapping is common in Yemen, with captives often being held as negotiating tools in disputes between rival tribes or armed groups.
Local journalists told the Gulf News website that loyalists of former President Ali Abdullah Saleh might have been behind the kidnapping.
Saudi Arabia and other Gulf Co-operation Council (GCC) states brokered the power-transfer deal that saw Mr Saleh relinquish power in November after months of anti-government protests and deadly clashes.
A Saudi foreign ministry spokesman said its embassy in Sanaa had contacted "the highest security authority in Yemen" about the abduction.
"They are investigating and trying to find out the reason," he added.
Earlier on Wednesday, Saudi Arabia announced it would provide Yemen with all its petroleum needs for two months.
The official news agency, Saba, announced the deal in its report of a meeting between King Abdullah and the Yemeni president Abd Rabbuh Mansour Hadi.
Attacks by armed groups on pipelines have hit Yemen's small oil industry hard, with both domestic and export production badly affected.