A well-known hypothesis, with far-reaching implications, is that biological evolution should preferentially lead to critical dynamic regimes. Useful information about the dynamical regime of gene regulatory networks can be obtained by studying their responses to small perturbations. The interpretation of these data requires the use of suitable models, where it is usually assumed that the system is homogeneous. On the other hand, it is widely acknowledged that biological networks display some degree of modularity, so it is interesting to ascertain how modularity can affect the estimation of their dynamical properties. In this study we introduce a well-defined degree of modularity and we study how it influences the network dynamics. In particular, we show how the estimate of the Derrida parameter from “avalanche” data may be affected by strong modularity.