The remains of Judge Mohammed al-Jirani were found on a farm in the town of Awamiya in the kingdom's Eastern Province, which has been a hotbed of protests among the Shiite minority for years.
The raid took place last Tuesday and subsequent DNA tests confirmed that a body recovered was that of Sheikh Jirani, a ministry spokesman told the official Saudi Press Agency.
The ministry named the slain suspected militant as Salman al-Faraj, adding that he was wanted on suspicion of terrorism offences.
Sheikh Jirani was kidnapped in December 2016 in front of his Awamiya home. The authorities said at the time that they had arrested three suspects.
Considered close to the authorities, the judge had been the target of several attacks before his abduction.
In a press conference Monday, interior ministry spokesman General Mansour al-Turki accused the judge's kidnappers and murderers of forming "an organised terrorist group that has relations with Iran and benefits from its support".
Saudi Arabia's council of senior scholars -- comprised of only Sunni clerics -- has decried the murder.
"This is a crime that must be condemned in the strongest terms and which reveals the threats posed by these terrorists," the committee said in a statement.
Sheikh Jirani was critical of the protest movement among his fellow Shiites and accused leading clerics in the community of being too close to Iran and neighbouring Iraq.
In 2011, his house and car were set on fire and members of his family barely escaped the flames. In 2012, his house was attacked again by armed men who failed to capture him.
Awamiya, a town of around 25,000 people, has seen bouts of unrest since 2011 when protesters emboldened by that year's Arab Spring uprisings took to the streets demanding an end to alleged discrimination by the Sunni-dominated government.
The Shiite community makes up between 10 and 15 percent of Saudi Arabia's population of 32 million.
A latest wave of unrest erupted in the summer when authorities began tearing down the historic Musawara district of Awamiya.
Authorities said that the walled neighbourhood's labyrinth of alleyways had become a breeding ground for "terrorists".
The demolitions prompted armed clashes between militants and security forces.
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