With high penetrations of renewable generation and variable loads, there is significant uncertainty associated with power flows in dc networks such that stability and operational constraint satisfaction are of concern. Most existing dc network optimal power flow (DN-OPF) formulations assume exact knowledge of loading conditions and do not provide stability guarantees. In contrast, this article studies a DN-OPF formulation, which considers both stability and operational constraint satisfaction under uncertainty. The need to account for a range of uncertainty realizations in this article’s robust optimization formulation results in a challenging semi-infinite program (SIP). The proposed solution algorithm reformulates this SIP into a computationally tractable problem by constructing a tight convex inner approximation of the feasible region using sufficient conditions for the existence of a feasible and stable power flow solution. Optimal generator setpoints are obtained by optimizing over the proposed convex stability set. The validity and value of the proposed algorithm are demonstrated through various dc networks adapted from IEEE test cases.