Sheikh Salih Ibn al-Luhaydan said some "evil" entertainment programmes aired by the channels promoted debauchery.
Dozens of satellite television channels broadcast across the Middle East, where they are watched by millions of Arabs every day.
The judge made the comments on a state radio programme.
He was speaking in response to a listener who asked his opinion on the airing of programmes featuring scantily-dressed women during the Muslim holy month of Ramadan.
"There is no doubt that these programmes are a great evil, and the owners of these channels are as guilty as those who watch them," said the sheikh.
"It is legitimate to kill those who call for corruption if their evil can not be stopped by other penalties."