So this message was appearing on some variety shows, as well as dramas….

番組をインターネットに許諾なく公開することは違法です

Rather than just giving you the English translation directly… let’s take a look at the meanings of each word used.
番組 (ばんぐみ, bangumi)
1. program (e.g. TV); programme
Straightforward enough.

インターネット – Internet
Also very straightforward

許諾 (きょだく, kyotaku)
1. consent

The word consent was followed by なく, adding a negative to the verb. I.e. No consent.

公開 (こうかい, koukai)
1. opening to the public; making available to the public; putting on display; exhibiting; showing (play, movie, etc.); holding (interview, etc.); open; public

すること would mean roughly ‘the act of’.

違法 (いほう, ihou)
1. illegal; illegality; invalid; unlawfulness

You can probably guess what they are saying by now.

“Making the program available to the public on the Internet without permission is illegal.”

Well there’s a tons of other ways to phrase it but the message and end result is the same. The TV stations has just put out a warning on their show!

They are serious about their copyright laws!

Definitions taken from jisho.org!