The former Portsmouth manager said that players face a fine of £1,000 per word if they step out of line.
"I had a rule at Portsmouth that anyone using Twitter or Facebook was not allowed to talk about the football club, their teammates or the supporters," Cotterill said.
"Otherwise they got fined £1,000 a word. If someone wants to write a nice paragraph with 20 words in it, then it'll cost them about £20,000 so I don't anticipate it happening again."
Cotterill's announcement comes after Forest striker Ishmael Miller took to Twitter over the weekend to criticise fans.
"It was something I'd have done anyway before what went on at the weekend," Cotterill said. "I don't want to single people out, it's gone on a bit before I came here, but I don't like anything like that."
"They can twitter about anything else, talk about their cars or anything else they want to do, but not about the club."
Cotterill debuts against Middlesbrough at home tonight after quitting Portsmouth last week.