In this paper, the feedback stabilization problem is investigated for non-linear differential-algebraic equation systems. The paper is composed of two algorithms, namely a regularization algorithm and a stabilization algorithm. It is shown that the feasibility of the regularization algorithm guarantees that there exists a feedback so that the closed-loop system admits a unique impulse-free solution. The application of the stabilization algorithm produces a set of new coordinates in which the original system can be expressed as a standard form. Based on the standard form, a stabilizing feedback is constructed, which guarantees that the closed-loop system admits a unique impulse-free solution and is locally asymptotically stable at the origin.