Four-times world champion Vettel went from fourth on the track to third and then back down to fifth after Formula One stewards applied post-race time penalties to Red Bull's Max Verstappen and then himself.
Vettel was demoted for making a dangerous move while braking as Red Bull’s Daniel Ricciardo tried to overtake.
The penalty was the first for the offence since drivers were given a written warning at the previous race in Texas about such 'defensive manoeuvres'.
“Scuderia Ferrari considers that a number of new elements have come to light after the decision was rendered that make the decision reviewable,” the team said.
Ferrari, third in the championship with Red Bull second, said it was aware the standings would not change but felt it was important to have clarity when a precedent was being established.
Race director Charlie Whiting had shown reporters video evidence earlier on Thursday at the Brazilian Grand Prix to address several controversies resulting from Mexico.
Whiting said stewards considered three key points regarding the Vettel incident - whether a driver had to take evasive action, whether an abnormal change of direction was made in the braking zone, and whether it was potentially dangerous.
“They felt Sebastian had moved under braking; that was very clear from the data, and also pretty clear from the video, of course,” he said. “It was potentially dangerous and it was an abnormal change of direction which could have led to an accident.”
Whiting added that footage from a track camera, which hardly anybody had seen, showed Vettel moving to the right and then, in the braking zone, to his left. He said the stewards had felt that was a potentially dangerous situation.
Vettel, who was also watching the video evidence, disagreed and said he moved once to defend his position and gave Ricciardo enough space on the inside.
“I kept the car straight for more than the majority of the braking so I think the reason why Daniel locked up so bad is because there was no grip on the inside,” he explained. “I think it actually looks a bit worse than it was.”
Original source: Ferrari challenges Vettel's Mexico penalty