An asymptotic theory is presented for predicting the sound field generated by small‐amplitude instability waves in low‐speed boundary‐layer flows. A Tollmien–Schlichting wave of fixed frequency, which evolves spatially in a Blasius boundary layer, is considered, and the associated far‐field acoustic radiation is calculated. It is found that the directional dependence of the radiation intensity is of the dipole type. This result is discussed in connection with the superdirective acoustic fields caused by instability waves, which were recently observed in low‐Mach‐number jets.