When time-reversal symmetry is broken (e.g., by a magnetic field), the viscosity tensor of a fluid will contain antisymmetric Hall-like components, in addition to the standard shear and bulk viscosities. For a gapped quantum fluid, such as the electron liquid in the quantum Hall regime, the Hall viscosity is predicted to be quantized, and to encode topological information beyond that provided by the Hall conductivity. Knowing its values could, therefore, help one differentiate between models for quantum Hall effect at different fillings such as 5/2. Furthermore, the Hall viscosity has previously been related to the conductivity in the presence of a spatially-varying electric field, which could be probed in an experiment. However, all these previous works were confined to clean systems, while any realistic system contains some disorder. In this work we bridge this gap by studying numerically the Hall viscosity and its relation to the conductivity for integer quantum Hall systems in the presence of disorder. Our results show that while disorder breaks the quantization of the Hall viscosity, the modification is small for not-too-strong disorder, making it feasible to extract the Hall viscosity from measurements on moderately clean systems.