Leclerc finished third at Sakhir after his car lost power with some 10 laps to go while he was leading the race comfortably.
Race winner Lewis Hamilton and his Mercedes team mate Valtteri Bottas both overtook the youngster before the chequered flag, with the Leclerc salvaging a podium place thanks to the safety car being deployed for the last three laps.
Ferrari said the problem had never been seen before on that particular component.
Leclerc had also started on pole position for the first time in his Formula One career, and in only his second race with Ferrari.
Shanghai will be the 1,000th Formula One championship grand prix and Ferrari will be favourites to win despite champions Mercedes finishing one-two against the odds in the first two races of the season.
(Reporting by Alan Baldwin in London, editing by Ed Osmond)
