Acoustic flame suppression is a potential technology which does away with the need to carry fire-extinguishing media and does not cause secondary pollution. We herein reported an experimental study on the displacement and extinction of jet diffusion flames exposed to speaker-generated traveling sound waves with a frequency of 110–150 Hz and local sound pressure of 2–16 Pa. The simultaneous movement of the flame and fuel was captured using a high-speed camera and schlieren techniques. Results showed that the flame oscillation was dominated by induced wind produced by membrane vibrations instead of sound pressure, and this induced wind’s frequency was the same as that of sound waves. Moreover, the movement of unburned fuel and flame was not synchronous, which resulted in an interrupted fuel–flame cycle. Consequently, the flame was gradually suppressed and completely extinguished after several oscillation cycles. Finally, we determined the extinction criterion that when the dimensionless gap between the flame and the unburned fuel was greater than or equal to 7, the flame would be extinguished. Results clearly revealed the mechanism of acoustic fire extinguishing, which provided reference for the feasibility of acoustic fire-extinguishing applications.