Sheikh Nimr's supporters say he advocated only peaceful demonstrations and eschewed all violent opposition to the government.
The cleric's nephew, Ali al-Nimr, who was 17 when he was arrested following the demonstrations and also faces execution, was not listed as one of those killed.
His brother, Mohammed al-Nimr, said he hoped any reaction to the execution would be peaceful.
Prominent Iraqi Shia cleric Moqtada al-Sadr called for "angry demonstrations in front of Saudi sites and interests", but said protests should be peaceful.
Lebanon's Shia council called the execution a "grave mistake" while the Hezbollah militant group said it was an "assassination".