Webber was forced to stop during the second period of the qualifying session at the Shanghai International Circuit, resulting in the 36-year-old Australian initially starting from 14th.
However, as Webber failed to drive back to the pits under the car's own power and provide a fuel sample as required, the FIA has been left with no choice but to penalise him.
Under the regulations, Webber is excluded from the qualifying results but is allowed to start from the back of the field or the pit lane.
Explaining their decision, an FIA statement read: "The team admitted it had not put sufficient fuel in the car.
"Only 150ml of fuel was on board, which was insufficient to provide the one litre sample and drive the car back to the pits under its own power."
The incident is almost identical to that incurred by team-mate Sebastian Vettel in last year's Abu Dhabi Grand Prix.
Vettel, however, was ordered by the team to stop his car on his in-lap after setting the third fastest time during qualifying at the Yas Marina Circuit.
On that occasion the team believed there was a problem within the fuel tank of the car, whereas in this instance an issue has been discovered with the fuel bowser.
Team principal Christian Horner said: "A frustrating qualifying session for the team and for Mark.
"Unfortunately in Q2 the amount of fuel that was required to be put into the car from the fuel rig was not fully delivered.
"This was due to an error with the fuel bowser that meant it under delivered three kilograms of fuel.
"Therefore on Mark's in-lap we saw large drop outs in the fuel tank collector and the car unfortunately ran dry of fuel, which is obviously frustrating.
"The fuel bowser has been immediately quarantined for further investigation.
"It's a shame as he would obviously have made Q3 today."
Webber has naturally admitted to being "very disappointed", and he now faces a tough ask simply to get into the points
"Q1 went okay, I was comfortable with the car and we had a good plan for the rest of the session," said Webber, who finished third in this race two years ago after starting 18th.
"But in Q2 we lost fuel pressure so I had to turn the car off and couldn't get it back to the pits.
"I had to stop on the circuit, so qualifying was over before it started really.
"We need a bit of luck now. It's not the optimum starting position, but we still have to try to get something from there."