Nimr and six other Saudi Shiites were sentenced to die and to have their bodies publicly displayed, the most severe penalty available to judges in the kingdom.
They were among 47 people put to death by Saudi Arabia on Saturday, an apparent message to Shiite anti-government protesters that the kingdom will brook no dissent.
Mohammed al-Nimr said residents of Saudi Arabia's eastern al-Qatif region, where most of the country's mainly Shiite Muslim minority live, were alarmed by the news.
"We were expecting and hoping that the voice of moderation and political settlements would prevail," Mohammed al-Nimr told Reuters by telephone. "We were shocked by this harsh news.
"Sheikh Nimr enjoyed high esteem in his community and within Muslim society in general and no doubt there will be reaction. We hope that any reactions would be confined to a peaceful framework," he said.
Nimr had long been regarded as the most vocal Shiite leader in Qatif, willing to publicly criticize the Al Saud ruling family and call directly for elections.
Mohammed al-Nimr said his family hoped the authorities would hand over the body of Sheikh al-Nimr for a speedy burial.
"There is nothing left between us and the authorities except this pure body. We hope it would be handed over as soon as possible."