Sheikh Nimr al-Nimr was a central figure in Shiite protests that erupted in 2011 as part of the Arab Spring, and any decision to carry out his execution would likely spark new unrest among the OPEC powerhouse's Shiite minority.
He was found guilty of sedition and other charges in October last year in a case that highlighted the limits on free speech in the kingdom.
Saudi King Salman must still sign off on the sentence before it is carried out.
"We hope a royal pardon will be issued," Mohammed al-Nimr said. "This verdict could cause major trouble ... Because my brother Sheikh al-Nimr is a prominent figure for Shiites, mainly in the Gulf."
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Last year's verdict in the Specialised Criminal Court found al-Nimr guilty of a host of crimes including, among others, incitement of vandalism and sectarian strife, failing to obey or pledge allegiance to then-King Abdullah, calling for the collapse of the state and insulting relatives and companions of the Prophet Muhammad. The court was set up in 2008 to handle terrorism cases.
Al-Nimr has not denied political charges leveled against him but says he has never advocated violence.
His supporters and rights groups see the case against him and other government opponents as an effort to silence dissent, particularly among members of the Shiite minority, many of whom are concentrated in the oil-rich east.
Sunni-ruled Saudi Arabia is embroiled in a sectarian-tinged rivalry with Shiite powerhouse Iran that is playing out in civil wars in Syria and Yemen, where the two countries support opposing sides. Riyadh is wary of what it sees as Iranian incitement among Shiites both at home and abroad, including in the neighbouring Shiite majority but Sunni-ruled kingdom of Bahrain.