Detecting small and local damages on structures based on ambient vibrations is a major challenge in structural health monitoring. However, being able to identify the minimum damage is essential for quantifying the effectiveness of the instrumentation and for defining the limitations of low-frequency vibration monitoring in general. This paper shows how subspace-based methods could be used by engineers to predict the minimum damage that can be detected. The method employs a Gaussian subspace-based residual vector as a damage-sensitive criterion and evaluates its deviation from zero mean through two different statistical hypothesis tests, a parametric version and a non-parametric one. A sensitivity analysis is carried out to parametrize the deviation from the nominal state, and link it to physical parameters in a finite element model through the Fisher information matrix. This link can also be used to predict the minimum detectable damage, e.g. by prescribing a minimum probability of detection based on code-based reliability concepts. Ultimately, the developed theory is verified by means of a numerical example.