Green made comments in the Scottish Sun where he used the term "my Paki friend" when describing his relationship with shareholder Imran Ahmad.
Show Racism the Red Card chief executive Ged Grebby said: "The comments of Charles Green are very ill-advised and someone in his public position should really know better than to use this kind of racist and offensive language.
"The use of the term 'Paki' is highly offensive and it something that we at Show Racism the Red Card are trying to educate young people against.
"For the CEO of Rangers to use the term in any context is not helpful as it sends out the wrong message to young people."
Green has hit back at the group stating that he feels that they have overreacted to his comments and that they've also been taken out of context.
"It is unfortunate that Show Racism the Red Card has fallen into the trap of taking something out of context and giving a knee-jerk reaction," he said in a statement.
"In the interview, I referred to the fact that we are now living in a politically correct world where words and phrases that were once used are no longer acceptable."
Rangers recently won the Scottish Third Division title.