Authorities have arrested 62 suspected members of the group, among them three foreigners, the ministry said in a statement carried by the official Al-Ekhbariya satellite channel.
Those arrested include 35 Saudis who had previously been detained on security-related allegations and released, it said.
Members of the organisation have "links with extremist elements in Syria and Yemen," it said, adding that authorities are still hunting down 44 others whose names have been submitted to Interpol.
The statement said "suspicious activities on social networks" had facilitated the arrests, without providing further details.
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It also includes the little-known Saudi Hezbollah Shiite militant group, as well as Shiite Huthi rebels fighting in neighbouring Yemen.
The ministry has said it will prosecute anyone who back such groups "financially or morally", or who seeks to promote them in the media and on social networks.
It also forbids "participation in, calling for, or incitement to fighting in conflict zones in other countries" as well as calling for demonstrations or taking part in them.
Members of that group went on to merge with Yemeni militants to form Al-Qaeda in the Arabian Peninsula, which is based in Yemen and seen as one of the network's most formidable affiliates.