Starting from 10th and 14th on the grid, Leclerc attempted an audacious move on Vettel on the approach to turn three of the Red Bull Ring.
But with little room for manoeuvre, Leclerc was forced onto the kerb from where his car was launched on to the rear of team-mate Vettel's SF1000.
The collision resulted in severe damage to the rear wing of Vettel's car, while Leclerc sustained front-wing issues that necessitated a change.
Four-time F1 champion Vettel managed to return to the pits where he was wheeled back into the garage and retirement, while the Scuderia crew put a new nose on Leclerc's car. The incident led to the safety car being deployed to clear debris.
Following a further three laps, however, Leclerc was forced to retire himself, with Ferrari confirming there was too much damage to the car.
It is the second time in four races the duo have come together, forcing both out of the race, as was the case in last year's Brazilian Grand Prix, while it is the first time Vettel has retired on lap one since the 2017 Singapore Grand Prix.
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