Mercedes’ Formula One championship leader Lewis Hamilton was declared the winner instead.
Significant and relevant new evidence that was not available at the time is required for a team to submit a ‘right of review’ under article 14 of the governing FIA's International Sporting Code.
The spokesperson said Ferrari, who last week dropped a planned protest against the penalty, had formally requested the review but gave no further details "due to the sensitivity of the matter".
Stewards will now have sole discretion to determine whether such a significant and relevant new element existed, with their decision final.
If the review is deemed admissible, a secondary hearing will be held.
Mercedes have won all seven races so far this season, and the last nine in total, with Britain's five times world champion Hamilton now 29 points clear of Finnish team mate Valtteri Bottas in the standings.
Vettel, who was furious with a decision that caused an immediate controversy, is 62 points adrift of Hamilton.
Formula One holds its eighth race of the 21 round season in the south of France this weekend at Le Castellet circuit, where the penalty is likely to remain a major talking point.
The Williams team requested a right of review last season against a three-place grid penalty handed to Russian driver Sergey Sirotkin, arguing that significant and relevant new elements had emerged. Stewards unanimously rejected the move.
(Reporting by Alasdair Mackenzie/Alan Baldwin; Editing by Ken Ferris)
