This paper investigates the problem of minimizing energy consumption for real-time video encoding on mobile devices, by dynamically configuring the clock frequency in the CPU via the dynamic voltage scaling (DVS) technology. The problem can be formulated as a constrained optimization problem, whose objective is to minimize the total energy consumption of encoding video contents while respecting a real-time delay constraint. Under a probabilistic workload model, we obtain closed-form solutions for both the optimal clock frequency configuration and the resulted minimum energy. We also compare the optimal solution with a brute force flat frequency configuration. Numerical results indicate that our derived optimal solution outperforms the brute-force approach significantly. Moreover, we apply the optimal solution for real-time H.264/AVC video encoding application. Our numerical results suggest that an energy saving of 10%-20% can be achieved, compared to the flat clock frequency scheduling.