Sheikh Mohammed al-Jirani, a judge, was abducted mid-December in a village in the Shia-majority eastern district of Qatif, a centre of minority unrest since 2011 in the Sunni-ruled kingdom.
State television has reported Jirani was critical of the unrest.
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Authorities have arrested three people who had been watching the judge before his abduction and an investigation allowed them to "identify three criminals who are directly implicated", the ministry said in a statement.
It called on the abductors to "immediately free" Jirani and said anybody with knowledge about the suspects who did not come forward would be prosecuted.
Shias in Saudi Arabia's oil-rich Eastern Province have long complained of marginalisation.
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