Ahmed bin Mubarak, top aide to President Abd Rabbuh Mansur Hadi, was abducted by gunmen Saturday morning, security officials said.
Houthi rebels "were forced to seize Mubarak and this was an important step to cut the way of any coup attempt on the peace and transition deal," said a statement by the rebels' political faction, Ansarullah.
Hadi appointed bin Mubarak premier back in October, but the rebels rejected the nomination.
A senior media adviser to the Houthi movement in Yemen, Osama Sari, told CNN that the presidential chief of staff had been detained by the Houthis as a message to the President.
Sari added this was because the President wanted to introduce a new constitution without the approval of the Houthis.
A Yemeni official close to the presidential administration also told CNN that the presidential chief of staff had been detained by armed men linked to the Houthi tribe.
The official said they believed the detention was linked to disagreement over the constitution. "This is force for political gain, a ridiculous show of muscle flexing," the official said.
The abduction comes amid rising tensions in the Arabian Peninsula country following the rise of Shiite Houthi rebels. Houthis swept into the capital last year, sparking battles that left more than 300 dead in a month.
In September, Houthis signed a ceasefire deal with the government. Since then, its members have installed themselves in key positions in the government and financial institutions.
Adding to Yemen's turmoil is al Qaeda in the Arabian Peninsula,
a terror group that has been exploiting and stoking the instability.
On Saturday, the Houthi media outlet, Al Maseerah, repeated the group's claim of responsibility.
The rebels further elaborated on their motives for the abduction in their statement.
"Surely there are series of steps the resistance forces will conduct to stop those powers from negligence and to stop their criminal activities against the people, today and in the future," the rebels' statement said, posted on Facebook.
"President Hadi must understand the sensitivity of the current situation and not be an umbrella for corrupt and criminal powers," the statement added.
The UK ambassador to Yemen and the U.S. Embassy in Sanaa called for bin Mubarak's immediate release.
"Very concerned about the kidnapping of Dr Ahmed Bin Mubarak. Few have done more to support the 2011 Revolution and ideals," Jane Marriott, the British ambassador to Yemen, said on Twitter
The "Revolution" refers to months of demonstrations and crackdowns that led to civilian deaths in 2011. Toward the end of that year, then-President Ali Abdullah Saleh resigned, and powers were transferred to then-Vice President Hadi.
Hadi was elected President in February 2012.. He was the only candidate on the ballot.