The agency quoted the interior ministry as saying that the man, identified as Sweilem al Ruwaili, had been hiding at one of his comrades from the "deviant group" in the northern al Jawf region when he was captured in the raid on Thursday.
Saudi Arabia uses the term deviant group to refer to extremist militants from al Qaeda or Islamic State.
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Ruwaili was on a list of 16 wanted people published by the kingdom last year in connection with two deadly mosque bombings claimed by Islamic State in May.
The authorities offered a cash reward of five million riyals ($1.3 million) for information leading to their arrest.
Islamic State has claimed responsibility for a series of bombings and shootings in Saudi Arabia since November 2014 that have killed more than 50 people.
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In August 2015, a suicide bomber killed at least 15 people in an attack on a mosque used by members of a local security force in southwest Saudi Arabia, in an assault that an online statement said was carried out by Islamic State.
A statement from the interior ministry said the woman had surprised security forces with a machine gun, and was subsequently hit in the raid and died in hospital of her wounds.
She had been married to another wanted man who "is in areas of conflict abroad", the statement said.
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