Demonstrators carrying pictures of the cleric, Sheikh Nimr al-Nimr, faced security forces in a standoff in the village of Abu-Saiba, west of the capital Manama, Reuters reported.
Activists have called for protests in the island kingdom.
Saudi Arabia executed 47 prisoners on Saturday, including Sheikh Nimr, a critic of the Riyadh regime who was arrested in 2012.
Sheikh Nimr was detained in July 2012 on charges of delivering anti-regime speeches and defending political prisoners.
His arrest sparked widespread protests in the Arab country, leaving several people dead.
In 2014, a Saudi judge found him guilty of “sedition” and sentenced him to death.
In October 2015, a Saudi appeals court upheld the death sentence, referring his case to King Salman’s office.