Sheikh Salih Ibn al-Luhaydan serves as the chairman of Saudi Arabia's Supreme Judicial Council. He made the comment about killing satellite TV purveyors in response to a question about racy TV shows broadcast during the Muslim holy month of Ramadan.
"The owners of these channels are as guilty as those who watch them," he said. "It is legitimate to kill those who call for corruption if their evil can not be stopped by other penalties."
BBC Arab affairs analyst Magdi Abdelhadi said that al-Luhaydan's views can't be easily dismissed because of his prominent standing in the country's legal community.
Abdelhadi also said that al-Luhaydan's support for executing what he sees as "immoral" broadcasters makes it difficult to fight militant Islam.
Judge al-Luhaydan's comments also caught the attention of luminaries across the Middle East — several Saudi princes own satellite networks.
The Saudi royal family has yet to comment on al-Luhaydan's statement.
The holy month of Ramadan is the ninth month of the Islamic calendar. It typically falls somewhere between August and October of the Gregorian calendar.