The defence ministry identified the Saudi who was arrested as Abdullah Faraj Mohamed Mahmoud al-Jawbar, who is on a list of 85 Saudis wanted by Riyadh.
The ministry said that authorities had found a suicide bomb belt in the house a week ago.
Death sentences upheld
Meanwhile, also on Sunday, a Yemeni appeals court upheld death sentences against four al-Qaeda fighters accused of carrying out attacks that included a deadly assault on the US embassy in March 2008 and the killing of two Belgian tourists in the same year.
A court official said the appeals court overturned the death sentences of two other alleged members of the same cell who were convicted of attacks on police in southern Hadramout province, and sentenced them to 12 years each instead.
The court in Sanaa on Sunday also upheld sentences of up to 15 years imprisonment against 10 other al-Qaeda suspects, including four Syrians and a Saudi man, for masterminding the attacks.
The cell was also accused of waging successive attacks on police and oil installations.
Most of the 16 fighters were arrested in August 2008 following a fierce gunbattle between al-Qaeda and Yemeni security forces in Hadramout.
Yemen is one of the poorest countries in the world and its government is already struggling to contain an uprising in the north, unrest in the south and the re-emergence of al-Qaeda in the region.