Ibrox supporters' group Sons of Struth said lawyers for the Rangers board members ordered them to remove posts from three individuals.
Sandy Easdale is chairman of Rangers Football Board, and his brother James is a board member.
The move comes less than a month after three members of the Rangers board - including the Easdales - lodged complaints with the police after allegedly violent threats were made against them.
In a statement, the fans' group confirmed they received a letter from the brothers' solicitors yesterday.
It read: "We received a letter from Peter Watson, solicitor advocate of Levy & McRae acting on behalf of Mr and Mr Easdale.
"The letter asked us to remove posts from three individuals."
The statement - posted on the Sons of Struth Facebook and Twitter pages - stressed that the posts did not come from the Sons of Struth group.
It continued: "We would like to remind posters that this is an open social network available to be viewed by the public.
"Posters should take care regarding defamation and The Offensive Behaviour at Football and Threatening Communications Act 2012."
A spokesman for Rangers said they would not comment on the issue.
However, he did confirm a letter had been sent to the Sons of Struth fans group.
Police Scotland said they had previously received complaints in relation to online threats to Rangers directors.
A spokeswoman said: "We are currently assessing if there is any criminality involved."