Towards the end of the race, the pair collided as they jostled for position, with Vettel attempting to regain fourth place which he lost to Leclerc at Turn 1.
As they headed down the straight towards Turn 4, slight wheel-to-wheel contact was made - however it was enough to deliver both drivers punctures and end their races.
"The Stewards reviewed video evidence and heard from the driver of car 5 (Sebastian Vettel), the driver of car 16 (Charles Leclerc) and the team representative," read a statement from the stewards.
"The Stewards determined that both drivers had the opportunity avoid or mitigate the incident and therefore that neither driver is predominantly at fault. Therefore the Stewards take no further action."
The double DNF for Ferrari was the first time since Singapore 2017 that the Scuderia outfit failed to score points in a race.
Bahrain International Circuit - Winter testing