In desalination plants, both measurable and unmeasurable process states play important roles in maintaining closed-loop stability and process operational performance. To effectively control the closed-loop system, an observer design that can estimate the values of the unmeasurable states is required. Motivated by that, in this paper we propose an observer design for an advanced water desalination technique called Direct Contact Membrane Distillation (DCMD). The DCMD process is modeled by a set of nonlinear Differential Algebraic Equations (DAEs). In addition, the effect of the estimation gain matrix on the differentiation index of the DAE system is investigated. Numerical simulations are presented to illustrate the effectiveness of the proposed observer design.