Recently, it has been reported that small‐scale (λ ∼ 0.1‐2 km) density irregularities occur during 100‐Hz electric field bursts in the nightside ionosphere of Venus. The correlation of field and plasma fluctuations suggests that a local plasma instability may be responsible for the turbulence. In this paper we provide a detailed analysis of the lower‐hybrid‐drift instability as a mechanism to generate the observed irregularities. We develop a fully electromagnetic theory that is relevant to the finite β plasma in Venus’ ionosphere and include collisional effects (e.g., electron‐ion, electron‐neutral, and ion‐neutral collisions). The key features of the analysis that favor this instability are (1) it is a flute mode and propagates orthogonal to the ambient magnetic field, (2) it is a relatively short wavelength mode and the Doppler‐shifted frequency can be ≳ 100 Hz, (3) it can produce both electric field and density fluctuations, as well as magnetic field fluctuations in a finite β plasma, and (4) it is most unstable in low‐β plasmas (i.e., β ≲ 1) so that it is likely to occur in the low‐density, high‐magnetic‐field ionospheric holes. These features are