Leclerc, 22, flew back to Monaco after Sunday’s Austrian Grand Prix and was even pictured in the principality standing next to a waiter.
The FIA investigated Leclerc’s movements and the incriminating Instagram image.
Ferrari driver Charles Leclerc was back in Austria on Thursday following his trip to Monaco
A spokesman for the governing body said: ‘We have issued a warning. Any further breaches will be referred to the stewards.’
The drivers and their 80-strong teams signed up to a code of conduct and almost all of them stayed in Austria between last weekend’s season-opening race and Sunday’s Styrian Grand Prix, also at the Red Bull Ring.
Everyone must stay in bubbles of two or three people.
Mercedes’ Valtteri Bottas also returned to Monaco to be with girlfriend Tiffany Cromwell
The code stipulates: ‘Any time outside the venue between covered events must be spent with other members of the same group, keeping interaction with persons outside that group to a minimum.’
The only other driver known to have flown home, again to Monaco, is Mercedes’ Valtteri Bottas, who is believed to have spent time only with his girlfriend, Tiffany Cromwell.
Lewis Hamilton has remained on site in Austria throughout.