Global vibration-based methods in the field of structural health monitoring are intended to capture structural stiffness changes of buildings or other civil engineering structures. Natural frequencies of buildings or bridges are commonly used parameters to monitor these stiffness changes. Therefore, it is essential to clarify the limit at which this method is no longer sensitive enough to be useful for structural health monitoring purposes. This paper numerically investigates the effect of structural damage and soil–structure interaction on cellular-type reinforced concrete buildings’ natural frequencies. These buildings are a common housing stock of Eastern Europe but are rarely investigated in this context. Comparisons with a reinforced concrete frame and infill structure building are made. Finite element models representing three structural system types of nine-story reinforced concrete buildings were used for the numerical simulations. Furthermore, a five-story finite element model was used for a damage sensitivity comparison. It is established that, for cellular-type structure buildings to detect damage comparable to that investigated in the paper, structural health (fixed base model frequency) should be monitored directly. Then, a statistical significance level for frequency changes of no more than 0.1% should be adopted. Conversely, the rocking frequency is a very sensitive parameter to monitor building base condition changes. These changes are often a cause of the cracking of building elements.