The blasts killed at least 22 people and injured scores more, Rajeh Badi, the spokesman for the new government, told CNN. All the Cabinet members are safe, according to Yemen Prime Minister Maeen Abdulmalek.
It is unclear if the explosions were caused by missiles fired on the airport. Badi told CNN that the investigations have not been concluded yet.
Saudi Arabia accused Iran-backed Houthi rebels of being behind the explosion, according to the state-run Saudi Press Agency (SPA). The group has not claimed responsibility.
Col. Turki Al-Malki, spokesman for the Saudi-led coalition in Yemen, said the coalition intercepted and downed an explosives-laden Houthi drone on Wednesday that was targeting the presidential Al-Maashiq Palace in Aden, according to SPA.
Al-Malki said the drone downing "confirms the responsibility" of the Houthi militia in the airport attack.
"The attempt to assassinate the Yemeni Cabinet is an attempt to thwart the Riyadh Agreement, which Yemeni people have adopted as a path toward unification of ranks, restoration of normal life, security and stability and a roadmap to reaching a comprehensive political solution in Yemen," Al-Malki was quoted as saying in a statement carried on SPA.
Earlier, Yemeni Information Minister Muammar Al Eryani accused the Houthi rebels of being behind the explosion.
Prior to the attack, hundreds of people had gathered at the airport for the arrival of the government, which was sworn in in Saudi Arabia last week.
The International Committee of the Red Cross (ICRC) said one of its staff was killed, three were injured and two others were unaccounted for in the explosions.
"Our staff were transiting through the airport with other civilians. This is a tragic day for us and the people of Yemen," the ICRC in Yemen said on Twitter. "We extend our sincere condolences to the families of the victims, and we hope for a speedy recovery for anyone injured."
Footage from Saudi-owned Al Arabiya channel showed the moment of the attack: A loud boom was followed by gunshots. Smoke was seen billowing out of the terminal building.