The detentions took place on Saturday and Sunday and followed marches by hundreds of people on Friday in Qatif and the neighbouring town of Safwa.
Local residents and a Shia website also reported the detentions, although interior ministry officials could not be reached for comment.
Public protests are banned in Saudi Arabia, although the authorities have shown unusual leniency in tolerating some marches against Israeli attacks in Lebanon.
The police did disperse a demonstration in the region on Thursday.
"They have arrested some of the participants in the recent marches and even relatives of others they could not find," said a Qatif resident who asked to be identified only as Munir.
Adil al-Labbab said one of his brothers was detained to put pressure on another to turn himself in.
"Such a practice is against international law, local law and even God's law," said Munir.
The kingdom, which fears the rising influence of Shia power in Iran, has denounced Israel's military campaign against Lebanon and called for a ceasefire, but has also blamed Hezbollah for provoking the conflict.
On Tuesday, more than 2,000 marched in Qatif to denounce Israel's offensive in Lebanon.