The Monegasque had qualified on the front row alongside Red Bull's triple world champion and pole sitter Max Verstappen, winner of 16 of the 19 races so far this season.
"I lost the hydraulics. Why am I so unlucky?" lamented Leclerc over the team radio after careering backwards into the barriers.
The race was then red-flagged following a collision at the start between Haas's Kevin Magnussen (31) and Williams' Alex Albon (27) that left debris scattered over the track.
Ferrari are in a battle with Mercedes for second place in the constructors' championship, with the Italians third and 24 points behind.
Leclerc said he first became aware of a problem when the steering wheel stopped responding and the car went straight ahead.
"I had no hydraulic any more. I don't think it's a hydraulic problem, I know what it is but I cannot go too much into detail," he told Sky Sports television.
"Then there was an engine thing that made me lock the rear wheels and then obviously I spun and hit the wall."
Leclerc said the issue was different to the hydraulics issue experienced by teammate Carlos Sainz (29) at the previous race in Mexico.
"I haven't gone into details with the guys but what they have seen is completely different and not what happened to Carlos," he said.
