The interior ministry said: the men had been monitored for several months before their arrest and "were on the verge of carrying out operations".
Police say: three of the men are from Yemen, one is still being identified and the rest are Saudis.
Correspondents say: Saudi Arabia has stepped up its security amid Islamic State's offensive in Iraq and Syria.
Interior ministry spokesman Mansour al-Turki did not give any details about the plots but said 59 of the men had previously served prison sentences for similar offences.
He told reporters the arrests were made over the past few days, and said it showed that Saudi forces were "serious in tracking down" anyone who joined extremist groups.
"It is unfortunate that some of those who had completed their sentences and were released by court orders returned to their previous ways," he added.
Those arrested support "misguided ideology and glorify terrorist acts," the spokesman added, saying several of them were in contact with "members of terrorist organisations" outside the country.
Earlier this year, Saudi Arabia made it illegal for its citizens to fight for groups overseas amid growing concerns that those citizens would eventually threaten the kingdom's stability.