It confirmed exclusively to Autosport that it was in no doubt that Vettel's pass was legitimate.
And F1 race director Charlie Whiting told German magazine Auto Motor und Sport that a green flag waved by the track before Vettel made his move overrides the flashing trackside warning lights which Ferrari were seeking clarification on.
The FIA confirmed that no further action would be taken.
"The incident wasn't reported to stewards in the first place because it didn't seem like there was a need to report it at the time," Norman Howell, FIA director of communications, said.
"Now that Ferrari has sent us a letter asking for an explanation we will give it to them."
Vettel was crowned champion for the third time at Interlagos after finishing in sixth position in an action-packed race in which he was spun after making contact with Bruno Senna on the opening lap.
Ferrari's Fernando Alonso finished in second position, a result that left him three points behind Vettel in the standings.
On Wednesday evening, however, Ferrari said it was reviewing video footage allegedly showing Vettel overtaking Vergne in a yellow-flag sector between Turns 3 and 4 early in the race.
The team stated on Thursday that it had written to the FIA asking for clarification over the matter.
Whiting said that the yellow-flag sector at Interlagos started at the light panel just before Turn 3, at marshal sector 3, and ends about 150m before Turn 4, where a green light panel is displayed.
However, there is a marshal's post in between these two panels and a green flag was being waved there on that lap.
Under the FIA's rules for the Brazilian GP, if a green flag is displayed before a green light - as it was in Vettel's case - it is the first green that counts.
Therefore, the FIA is in no doubt that Vettel's pass was legitimate, which is why race control was not informed of any potential infringement.
The FIA confirmed to Autosport that no team had asked for a review of the incident. The ruling body also said it does not comment on the stewards' decisions.
"The request for a clarification from the FIA, regarding Vettel's passing move on Vergne, came about through the need to shed light on the circumstances of the move, which came out on the Internet only a few days after the race," Ferrari said in a statement on their website.
"The letter to the FIA was in no way intended to undermine the legality of the race result. We received tens of thousands of queries relating to this matter from all over the world and it was incumbent on us to take the matter further, asking the Federation to look into an incident that could have cast a shadow over the championship in the eyes of all Formula 1 enthusiasts, not just Ferrari fans.
"Ferrari duly takes note of the reply sent by the FIA this morning and therefore considers the matter now closed."