The 79-year-old Sheik Saleh al-Lihedan said Thursday that satellite channels cause the "deviance of thousands of people."
Many of the most popular Arab satellite networks - which include channels showing music videos often denounced as obscene by Muslim conservatives - are owned by Saudi princes and well-connected Saudi businessmen. Al-Lihedan did not specify any particular channels.
Al-Lihedan is chief of the kingdom's highest tribunal, the Supreme Judiciary Council. Saudi Arabia's judiciary is made up of Islamic clerics whose decrees, or fatwas, on everyday issues are widely respected. Their fatwas do not have the weight of law. In the courts, cleric-judges rule according to Islamic law, but interpretations can vary.
Al-Lihedan was answering listeners' questions during the daily "Light in the Path" radio program in which he and others make rulings on what is permissible under Islamic law.
One caller asked about Islam's view of the owners of satellite TV channels that show "bad programs" during Ramadan.
"I want to advise the owners of these channels, who broadcast calls for such indecency and impudence ... and I warn them of the consequences," he said.
"What does the owner of these networks think, when he provides seduction, obscenity and vulgarity?" he said.
"Those calling for corrupt beliefs, certainly it's permissible to kill them," he said. "Those calling for sedition, those who are able to prevent it but don't, it is permissible to kill them."
Among the most viewed Arabic satellite networks is Rotana, which airs movies and music videos. It is owned by Prince Al-Waleed bin Talal, a billionaire businessman and member of the royal family whom Forbes ranks as the world's 13th richest person.
Other questions in the radio show tackled personal issues. Al-Lihedan advised one man, for example, that by kissing his wife during the day he broke his fast during the holy month of Ramadan, when having sex, eating, drinking and smoking are prohibited from sunrise to sunset. He told the man he should make up for it with an extra day of fasting.
Al-Lihedan sparked controversy in the past by issuing a decree that Saudis can join jihadists to fight U.S. troops in Iraq.