B737-800 Captain reported a critical ground conflict with a fast moving fuel truck on a collision course with aircraft. Captain stopped immediately avoiding a collision.

Narrative

Taxiing on the uncontrolled ramp from gate to spot; contacted Ground for taxi. Ground gave instructions to XXC; via taxiways. Continued taxi; and as we were passing YC; I cleared left. The First Officer (FO) called out 'Stop!' a couple of times. I applied brakes; stopping the aircraft; and looked right. A fuel truck was approaching at a high rate of speed; and it swerved hard left; nearly overturning as its left wheels left the ground. We are almost convinced the truck was about to roll over. It successfully completed its turn; and we notified Ground that we had a truck almost cut in front of us; then continued our taxi to XXC. We completed the flight without incident. The Flight Attendants (FAs) were prevented from falling and hurting themselves during pre-takeoff duties by passengers catching them; or catching themselves. No one was hurt; and no internal aircraft or equipment damage. The fuel truck was traveling far too fast; and the awareness of aircraft on an active taxiway was obviously absent.