Owens responded by mocking McDonald and saying he didn't know who McDonald is.
During his press conference Monday afternoon, Browns coach Eric Mangini said he is aware of the Twitter controversy. Mangini said he talked to his players Monday morning about their use of social media.
"With social media, it's a great way to connect to the fans, and (players) have a responsibility to do that in a way that represents the organization the right way," Mangini said. "And that's their responsibility, and they're accountable for it. If they don't do it, there are consequences to those actions. We talked about that as a group.
"I don't expect people to stop using. I think it is a good way to communicate to our fans. ... But like with anything else that you do, you have to do it in a right way and a way that represents the organization the right way."