The televised match, which was set to be played on Sunday at lunchtime, was called off on Friday after too many tickets were sold.
Moray Council, Grampian Police and the Scottish Football League took the joint decision to postpone the fixture at Borough Briggs on safety grounds after it emerged that at least 1,100 extra tickets had been sold.
Fans have been assured they will be given a full refund but, naturally, tickets issued for Sunday's game will not be valid for the re-arranged date, which has yet to be announced.
A statement from Elgin read: "Following a meeting of the Elgin City board this morning, we can confirm that a full investigation into the over-sale of tickets for the postponed match this Sunday against Rangers is ongoing.
"The club officials are working closely with Grampian Police, the local authority and the Scottish Football League to establish the full facts in this matter.
"We would ask all fans to note that tickets issued for the game due to be played on Sunday 25th November 2012 will not be valid for the re-scheduled date.
"The club advises that those holding tickets issued by Elgin City return these to the club for a full refund.
"Tickets purchased via Rangers FC for this match should contact the Rangers ticket office.
"Elgin City FC office will be open to refund tickets on Monday 26th and Tuesday 27th November during the hours of 12.30pm to 2.30pm and 6.30pm to 8.30pm.
"The club are aware that not all fans will be able to attend at these times but would assure all ticket holders that the process will be ongoing during normal office hours until all monies have been refunded.
"New ticketing arrangements will be announced in due course once a rescheduled date has been announced by the Scottish Football League.
"Once again Elgin City Football Club wishes to apologise sincerely to all fans and the local community for the postponement of this game."