In this paper, we generalize the cooperative output regulation problem of multi-agent systems, and we consider the case where agents in the system only receive incomplete measurements from the exosystem. In other words, we consider the case where no agent receives sufficient information through its measurements to estimate the exosystem states. Under certain intuitive assumptions on the connectivity between the agents and their combined detectability property, we propose a distributed control law that solves the cooperative output regulation problem under the considered problem constraints. A numerical example is offered to illustrate the effectiveness of the proposed control solution.