Mohammad bin Saeed Al-Amri was carrying a pipe bomb when he was arrested along with two other men on Monday, the ministry said in a statement carried by the official Saudi Press Agency.
Al-Amri, 25, was named by Saudi authorities last month in a list of 36 wanted militants. The ministry offered rewards of up to 7 million riyals ($1.87 million) to anyone who helped capture any of the men or foil any planned attack.
The ministry said al-Amri was seized after a group of Saudi citizens became suspicious and contacted authorities.
Saudi Arabia has been battling a two-year wave of violence by supporters of Saudi-born Osama bin Laden's al-Qaida network.
Syria has extradited to Saudi Arabia 12 "extremists" linked to a slain Tunisian militant, who it said had planned to set up a training camp for militants on Lebanese territory, the state news agency SANA has said.
The agency did not reveal whether the 12 were Saudi nationals or when they were handed over, but said it was the first of several planned extraditions of an unspecified number of militants to their countries of origin.
"The Syrian authorities have started to extradite a number of extremists who are in their custody and who belong to several Arab nationalities to their respective countries," SANA said.
It said the militants had been involved in a clash on the Syrian-Lebanese border on 22 June, when a Tunisian, identified by the media as Majdi bin Mohammad bin Said al-Zreibi, was killed.
The agency referred to the Tunisian only by his initials.
Syria announced this month that its forces had killed an Arab Muslim militant who was among a group trying to cross the border into Lebanon and had arrested at least 34 others.
"The Syrian authorities have started to extradite a number of extremists who are in their custody and who belong to several Arab nationalities to their respective countries"
Syrian Arab News Agency
The militant, apparently al-Zreibi, was killed in a clash on the Syrian side of the northeastern Lebanese-Syrian border.
Lebanon's al-Manar television station said at the time that the militants had been intercepted on their way from Iraq to Lebanon.