Thermoacoustic instability in a fluid monolayer complex plasma is studied for the first time. Experiments, theory, and simulations demonstrate that nonreciprocal effective interactions between particles (mediated by plasma flows) provide positive thermal feedback leading to acoustic sound amplification. The form of the generated sound spectra obtained both in experiments and simulations excellently agrees with theory, justifying thermoacoustic instability in the fluid complex plasma. The results indicate a physical analogy between collective fluctuation dynamics in reactive media and in systems with nonreciprocal effective interactions exposing an activation behavior.