The Newcastle United owner owns an 8.92 per cent stake in Rangers, and has been prohibited from increasing that beyond 10 per cent.
In January, it was announced the cash-strapped club would borrow £10 million from Sports Direct, the retail company owned by Ashley.
Five Newcastle players have been loaned to Rangers, who are bidding to return to the Scottish Premiership after their financial woes saw them drop to the Third Division in 2012-13.
Last month, manager Kenny McDowell claimed he was obliged to select the players.
On Tuesday, a statement from the SFA declared Ashley had been fined after breaching rules which state "no person who is involved in any capacity whatsoever in the management or administration of a club...may at the same time either directly or indirectly (a) be a member of another club; or (b) be involved in any capacity whatsoever in the management or administration of another club; or (c) have any power whatsoever to influence the management or administration of another club."
A second alleged breach, relating to whether Ashley had acted in the "best interests of Association Football", was not proven.
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