The two smaller groups were made up of 11 Saudis and a Yemeni, who security officials described as being a prominent member of al-Qaeda.
The groups had links to an al-Qaeda affiliate based in neighbouring Yemen, Mansour al-Turki, a ministry spokesman said.
He said a "network" and two cells working independently of each other had been uncovered.
The large cell was discovered as the result of an investigation launched after suspected al-Qaeda fighters - two of them dressed as women - tried to infiltrate the country in October with explosives.
The two were killed in a shootout at the border and a third was arrested.
Al-Turki said the investigation had so far revealed "correspondence between this organisation and al-Qaeda's organisation in Yemen".
He said weapons, cameras, documents and computers were also seized.
"The network and the two cells were targeting the oil facilities in the Eastern Province and they had plans that were about to be implemented," al-Turki said.
The foreigners in the cell were said to have entered the country under the pretence of seeking work or visiting Muslim holy sites in Mecca and Medina.
There has been no official disclosure on which oil installations were being targeted and whether they were foreign or Saudi-owned.
"We seized belts of explosives which they were planning to use in suicide attacks," a security official said.
|Those arrested included 58 Saudis and 55 foreigners - mainly from Yemen [EPA]
Most of the suspects were arrested in the southern province of Jazan, near the border with Yemen.
The dates of the arrests were not disclosed.
In 2003, suicide bombers suspected of having links with al-Qaeda killed 35 people in the capital Riyadh.
But a security crackdown helped curb violence inside the kingdom after 2006.
In 2007, officials said 172 terror suspects had been arrested; and in August 2009 44 suspects with alleged links to al-Qaeda were detained.
Hussein Shobokshi, a columnist for the Asharq Alawsat newspaper, told Al Jazeera Saudi Arabia is winning the battle against al-Qaeda in the kingdom.
"By the sheer fact that they have arrested them and exposed their cells before any acts were committed proves that the preventive acts of the Saudi security forces have been effective," he said.
"The number of those arrested is alarming indeed and the soft pocket that exists in the southern border of Saudi Arabia with Yemen is an alarming concern."
Riyadh is especially concerned about the resurgence of al-Qaeda in the Arabian Peninsula (AQAP) in Yemen.
In September, Michael Leiter, the director of the US National Counterterrorism Centre (NCTC), said the AQAP had gained a dangerous foothold in Yemen.
"We have witnessed the re-emergence of al-Qaeda in the Arabian Peninsula, with Yemen as a key battleground"
Director of NCTC
"We have witnessed the re-emergence of al-Qaeda in the Arabian Peninsula, with Yemen as a key battleground and potential regional base of operations from which al-Qaeda can plan attacks, train recruits and facilitate the movement of operatives," Leiter said.
Earlier this month, Saudi Arabia's King Abdullah said the kingdom is determined to halt extremism.
"In domestic policy, the government continues to expend its efforts to strengthen security," he said in his annual speech to the Shura Council, the country's consultative assembly.
"A special effort has been made to confront the thinking of the group of deviants, extremists and terrorists," he said, using language the government usually employs to identify al-Qaeda.
"The security services have had repeated successes with preventative actions, and will continue their activities to foil the terrorist plots, eradicate the deviant groups, and dry up the sources of terrorism."