Air carrier Captain reported the aircraft became disconnected from the push-back tug during push back and rolled backwards. Captain set parking brake and stopped aircraft movement.

Narrative

Uncontrolled ramp. Guide-person reported ready to push. I released the parking brake and cleared the guide person to push. As the aircraft began to move backwards I saw the Gate Agent standing in the jetway gesticulating and told the push crew to stop the push. The push crew responded with 'set brakes; set brakes; set brakes'. Concerned about hitting someone or something I set the parking brake while the aircraft was in motion resulting in an abrupt stop. A few minutes went by before I could reestablish communications with the tow tractor driver. I asked what was going on. This tow tractor was the type that captures the nose wheel of the aircraft and I was told that there was some kind of malfunction and the tow tractor had released the nose wheel. The aircraft had been coasting backwards. I'm not sure; but we probably rolled back 15-20 ft. I was assured that the situation had been remedied; there was no damage or injuries; and that the push crew was once again ready to push. The flight attendants were standing; giving the safety demonstration; at the time I set the parking brake but reported that they were ok. We started over with the guide persons report and continued the flight without further incident.I think there was training going on with the Tow Tractor Operator. I suspect that there was Operator error versus a malfunction. Not sure; since I don't know exactly what went on with the tow tractor. 'Set brakes' was absolutely the right thing for the Tractor Operator to say. I think the outcome of this incident was quite good all things considered.