The Ferrari driver was penalised 10 seconds for moving while in the braking zone while defending from Red Bull's Daniel Ricciardo late in the race.
The 29-year-old also had two penalty points added to his racing licence.
Vettel had been promoted to third after Ricciardo's team-mate Max Verstappen was penalised for cutting a corner.
Four-time champion Vettel had indicated after the race that he realised there may be a problem with his defence against Ricciardo.
"I want to look at it again; he [Ricciardo] told me to. I am fighting hard and am supposed to give him just enough room," Vettel said.
"I know Daniel is sometimes optimistic going for a gap. I knew he would go for it whatever the cost. I tried to defend; we made contact. That is not ideal. That's why I want to look at it again.
"If there was something, I will talk to him. Before that, Max was brake-testing me into the first two corners. I was very upset with the fact Max held me up and didn't move and made me run into Daniel."
Ricciardo said before learning of the penalty: "He doesn't deserve to be up there. I thought I had every right to be there but he kept closing the door under braking. I was frustrated with that."
The rule Vettel broke was only introduced specifically at last week's US Grand Prix.
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It was a rule clarification issued by race director Charlie Whiting on a specific issue that has caused controversy this year because many drivers felt Verstappen had transgressed their gentleman's agreement not to move under braking.
Ironically, Vettel was one of the prime critics of Verstappen's driving.
The new clarification states: "Any change of direction under braking which results in another driver having to take evasive action will be considered abnormal and hence potentially dangerous to other drivers. Any such move will be reported to the stewards."
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Sebastian Vettel lost third place in the Mexican Grand Prix after becoming the first driver to be punished under a new dangerous driving rule.