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We present MLNav, a learning-enhanced path planning framework for safety-critical and resource-limited systems operating in complex environments, such as rovers navigating on Mars. MLNav makes judicious use of machine learning to enhance the efficiency of path planning while fully respecting safety constraints. In particular, the dominant computational cost in such safety-critical settings is running a model-based safety checker on the proposed paths. Our learned search heuristic can simultaneously predict the feasibility for all path options in a single run, and the model-based safety checker is only invoked on the top-scoring paths. We validate in high-fidelity simulations using both real Martian terrain data collected by the Perseverance rover, as well as a suite of challenging synthetic terrains. Our experiments show that: (i) compared to the baseline ENav path planner on board the Perserverance rover, MLNav can provide a significant improvement in multiple key metrics, such as a 10x reduction in collision checks when navigating real Martian terrains, despite being trained with synthetic terrains; and (ii) MLNav can successfully navigate highly challenging terrains where the baseline ENav fails to find a feasible path before timing out.