With 15 minutes to go in first free practice, Vettel suffered a loss of power, forcing him to pull up his AMR22 car at the side of the track at Turn 10.
After the chequered flag, Vettel used a marshal's scooter to make his way back to the pitlane, running on the final sector of the track.
The FIA soon launched an investigation as Vettel was deemed to have re-entered the track within five minutes of the end of a session without permission.
On Friday night the stewards handed the German a 5,000 euro fine for his scooter-based adventure.
Vettel said he had received permission from the marshal to use the scooter to enter the circuit, but the stewards deemed that neither he nor the marshal had received approval from race control to use the circuit itself rather than the usual perimeter road.
That meant the four-time world champion breached Article 26.7 of F1's sporting regulations, which will cost him a 5,000 euro fine.
The FIA statement read: "At the end of the session, VET sought a way to return to his pit. A marshal was at the location with a scooter. VET asked if he could drive the scooter in order to return to his pit. The marshal assented. VET got on the scooter, expecting the marshal to get on behind him.
"When he didn't get on, VET departed alone for the pit, without the prior approval to do so. Meanwhile, the marshal was trying to contact Race Control for instructions.
"In driving on the track to his pit, instead of the designated route, VET breached Article 26.7 of the Formula One Sporting Regulations, which prohibits anyone from being on the track in the five-minute period after the end of a session, with the exception of specifically identified personnel, which makes no provision for drivers to have such access unless specifically authorized."
Vettel, who is making his first 2022 grand prix appearance after sitting out the first two races of the season with COVID-19, took the opportunity to greet the fans on his leisurely scooter ride back to the paddock.
After placing 13th in FP1, Vettel took no part in second free practice, Aston Martin deciding to swap his Mercedes engine following the issue.