Following Australia's 231-run defeat in the second Test in Port Elizabeth last week, Warner said South Africa - and wicketkeeper AB de Villiers in particular - had deliberately scuffed the ball to encourage reverse swing.
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The International Cricket Council subsequently fined the opener 15 per cent of his match fee and, ahead of the start of the third and deciding Test in Cape Town on Saturday, Clarke said he was "disappointed" with Warner's comments, and revealed his team-mate will be punished internally.
Clarke refused to reveal details of the penalty, and also made it clear he has no problem with South Africa's conduct.
"I don't have any dramas with the way they play their cricket," the skipper said.
"I think they play a great brand of cricket, they play a similar brand to us - they're extremely tough to beat on the field.
"I've had some of my toughest battles against South African players and, in particular, Graeme Smith, who I get on well with.
"I think he's a lovely fella, I think he's a great captain and I enjoy the challenges that I have against South Africa.
"As long as people understand and respect that, from inside this changing room, there is a lot of respect there and we certainly know that we have to be at our best to beat the best team in the world."