We analyze the class of networks characterized by modular structure where a sequence of l Erdos-Renyi random networks of size N >> 1 with random average degrees is joined by links whose structure must remain immaterial. We find that traceroutes spanning the entire macronetwork exhibit scaling degree distributions P(k) similar to k(-gamma), where gamma depends on how the degrees of the joined clusters are distributed. We thus suggest that yet another mechanism for the dynamic origin of arbitrary power-law degree distributions observed in natural and artificial networks, many of which belong to the range 2 <= gamma <= 3, may be found in random processes on modular networks.