"I don't understand it, to be honest with you ... there are a million things you can do with your life other than that," Ferguson told a news conference when asked about the social networking site where some of his players are prolific tweeters.
"Get yourself down to the library and read a book. It's a waste of time."
The Premier League champions' players could find themselves banned from using Twitter altogether after Ferguson said the club were examining its use.
"It seems to have a certain momentum at the moment. Everyone seems to want to do it," the 69-year-old Scot said.
"We as a club are looking at it because there can be issues attached to it. And we don't want that."
Ferguson's comments came after Rooney had been involved in an exchange where he had written "I'll put u asleep within 10 seconds u little girl" to a series of abusive postings from another user.
Rooney has more than half a million followers, while defender Rio Ferdinand has more than a million and tweets several times a day.
It did not take Ferdinand long to respond to concern over his tweeting future - via Twitter of course.
"Relax we have not been banned from social network sites... I think the powers that be are going to look at boundaries etc," he wrote in response to a post by British businessman-cum-television personality Alan Sugar.
