Non-executive chairman Walter Smith left the Scottish League One club on Monday after Green was given a new consultancy role last week.
On his own departure from Ibrox last summer, former coach Brown addressed a gathering of Rangers fans outside the stadium and spoke of his concerns about Green taking control of the club.
Brown's calls were ignored, and the 51-year-old fears it may be too late for the Rangers supporters to save their club from liquidation.
He said: "It's a ticking time-bomb. There's in-fighting in the boardroom. My biggest fear is that Rangers will go back into administration because of what's going on.
"Charles Green was never away. He might have had an extended holiday but he was never away because the people who are running Rangers are putting him up front.
"Rangers will suffer and they will continue to suffer until they sort it all out. It's a nightmare scenario.
"Sooner rather than later there will be no money left. Bang, they will be out of business. Rangers will go down unless the fans stand up and say enough is enough. That's the only way."