Monaghan, who played Charlie Pace on the series, was seen to be answering questions on a verified Twitter account set up in his name when a Lost fan asked him to tell Fox to join the social networking site.
© WENN
Without offering any evidence to support the claims, the actor's account responded: "he beats women. No thanks. (sic)."
The fan, surprised by this proclamation, asked: "WHAT ABOUT ALL THOSE GOOD TIMES YOU HAD TOGETHER?!"
Monaghan answered: "how do you know we ever did?you don't know either of us. he beats women. not isolated incidents. often. not interested."
The 35-year-old's profile then received a number of comments from angry Lost fans, with one writing: "How classy. Hope Matthew Fox sues you for defamation."
Monaghan replied: "it's very difficult to sue someone for speaking the truth."
Fox was accused of assaulting a woman outside an Ohio bar last September.
Criminal charges were not brought against him but the woman later filed a civil suit against him. Fox has countersued, claiming that the woman hit him.
No other public allegations of violence have been made against the 45-year-old.
Fox was arrested on suspicion of driving under the influence earlier this month. He has since been charged and will appear in court on Thursday, June 7.
