The governing body will investigate whether there have been any potential breaches of their Articles of Association.
The SFA say attempts to obtain information relating to their "fit and proper person" requirement - regarding Rangers owner Craig Whyte - have been restricted by the club solicitors' failure to share information.
Rangers were forced into administration on Tuesday over an unpaid tax bill of #9 million accrued since Whyte`s takeover of the club in May.
An SFA statement read: "The Scottish FA can today [Friday] confirm its intention to conduct a full independent inquiry into the activities of Rangers FC and, specifically, a number of potential breaches of the Scottish FA's Articles of Association.
"We are concerned by the developing situation at the club and the new information that has come to light since the appointment of the club administrators, Duff and Phelps.
"The chairman and his panel will be briefed by the chief executive, Stewart Regan, next week and will consult further with the administrators, Duff and Phelps, as part of their inquiry.
"We have been guaranteed full co-operation by Paul Clark, representing the company.
"The Scottish FA's previous efforts in obtaining information relevant to the Fit and Proper Person requirement has been restricted by the club's solicitors' continued failure to share information in a timely or detailed manner.
"We now feel there is no option but to undertake an independent inquiry to establish the clear facts and to determine the extent of any possible rules breaches."
SFA chief executive Stewart Regan said: "Since we have been unable to receive any detailed information requested in relation to Article 10, we feel we have no option but to appoint an independent committee to investigate a number of concerns we have raised.
"We expect the investigation to be concluded as quickly as possible and will confirm the outcome in due course. We will be making no further comment on the investigation in the meantime.
"Finally, I would like to reiterate the need to learn the lessons from this unedifying episode.
"It is essential that we work together to improve the overall sustainability and competitiveness of the game in this country.
"This is a matter that the Scottish FA is already in discussions with the relevant league bodies to address."