In this paper, we propose an observer-based distributed protocol for solving the output containment problem in linear heterogeneous multi-agent systems under the external disturbances. The distinct feature of the proposed protocol is that it does not require exchange of the internal controller states, which significantly reduces or completely eliminates communication burden. A sufficient local stability condition is derived and a novel controller design procedure is proposed based on tools from H∞ theory and algebraic Riccati equations. An extensive solvability analysis of the output containment control problem under the proposed protocol is carried out and theoretical guarantees for the existence of a solution for a wide class of agents’ dynamics and graph topologies are established. Numerical simulations that demonstrate the effectiveness of the proposed protocol are performed.