Ahmed Awad bin Mubarak and two of his guards were kidnapped early on Saturday in the centre of the capital Sanaa.
Yemeni officials suspect Shia Houthi rebels, who control much of the capital, of being behind the abduction.
Yemen has been plagued by instability since mass protests forced former president, Ali Abdullah Saleh, to step down in 2011.
Scores of people have been killed in clashes between the Houthis and Sunni militants.
One source told Reuters Ahmed Awad bin Mubarak was kidnapped by the Houthis to stop him presenting a draft of the new constitution to a presidential meeting.
The rebels blocked Ahmed Awad bin Mubarak’s appointment as prime minister last year.
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