Al-Watan newspaper quoted unidentified security sources as saying the suspects were captured overnight on Thursday during a raid on a house in Karboush village near the town of Jizan, 30km from the Yemeni border.
It said weapons and ammunition were found in the house and that no casualties were sustained during the raid.
Saudi officials could not immediately confirm the report.
Al-Watan said the arrested men could be linked to a group of Islamists that clashed with security forces in the capital Riyadh last Tuesday, killing four police officers and two of their own number.
The newspaper said police were tipped off by Saudi citizens before they raided the hideout.
Saudi Arabia's Crown Prince Abd Allah Bin Abd al-Aziz urged Saudis on Thursday to cooperate with the kingdom's "anti-terror" drive, saying anyone who cooperated with the "terrorists" was a "terrorist" himself.
Saudi Arabia has come under intense US pressure to clamp down on Islamists after the September 2001 attacks said to have been carried out by mainly Saudi hijackers loyal to Saudi-born fugitive Usama bin Ladin.
This pressure intensified after triple suicide bombings in Riyadh in May gutted housing compounds for foreigners, killing 35 people including nine Americans.
Since then Saudi Arabia has launched a severe crackdown on Islamists, leading to a series of arrests and bloody clashes in which 16 suspects and 11 Saudi police have been killed.