Kenny sent texts and left voicemail messages with QPR owner Tony Fernandes and chief Mike Rigg, impersonating Robert Green's agent and claiming he will "come good" after last week's mauling by Swansea City.
Warnock told The Independent: "I was disappointed that something that began in good humour got out of hand.
"I've spoken to Paddy Kenny and he was full of remorse and couldn't apologise to me quickly enough. I told him there is no problem with having a drink to celebrate a win like last Saturday's over Wolves but he must be aware of his responsibilities to the club and be careful where he is and what he does.
"I've fined him and he has agreed to finish on Twitter with immediate effect. He has also apologised to Tony Fernandes. I've also spoken to Tony and told him I honestly believe there will not be a repeat. We ended the call on good terms."