The visit of Ally McCoist's side was called off on safety grounds by Grampian Police after it became clear the Black and Whites sold too many tickets for their Borough Briggs ground.
A meeting of the SFL's board will today decide whether to invoke rule 98.4, which could result in points being deducted.
An SFL spokesman said: "Potentially they could be docked points."
Elgin are currently second top of the table on 22 points, just two behind leaders Rangers.
Rule 98.4 states: "Any club without just cause failing to fulfil its fixture obligations in respect of any such match under the jurisdiction of the League on the appointed date or dates shall for each offence be liable to the deduction of points in respect of a League Championship match, and/or to such other punishment as the Board may determine."
Elgin could also be hit by a compensation claim by Rangers, with league rules stating any expenses incurred as a "direct result of the failure" should be paid.
The SFL board determines the amount of compensation due in such a case.
SFL David Longmuir promised there would be a full investigation into the circumstances of the cancellation.
"We made a decision late on Friday afternoon to call the game off on the grounds of public safety," he said. "We should not have to deal with Elgin to make clubs realise that this should not happen.
"I've asked them to furnish me with a full report of the circumstances that brought the game to be called off and I'll look at that in conjunction with the report I get from my operations manager and our board will make a decision, if any, in a very short time scale."