The decision, announced by the court on Wednesday, is in line with an earlier decision made last year that dismissed appeals brought by British American Tobacco (>> British American Tobacco plc), Japan Tobacco International and Imperial Brands (>> Imperial Brands PLC).
The companies had argued that the law, which went into effect last May with a one-year grace period for existing inventory to be phased out, unlawfully deprived them of intellectual property by banning the use of all marketing on packages, including logos, colours and special fonts.
In its latest decision, the Supreme Court said the refusal to hear the appeal was based on the fact that it did not "raise a point of law of general public importance which ought to be considered at this time, bearing in mind that the case has already been the subject of judicial decision and reviewed on appeal."
Officials at BAT and Japan Tobacco International were not immediately available for comment.
The new law aims to discourage the deadly habit with drab-coloured packaging and large pictorial health warnings.
(Reporting by Martinne Geller, editing by Louise Heavens)