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In this paper, we study resource allocation algorithm design for secure multi-user downlink ultra-reliable low latency communication (URLLC). To enhance physical layer security (PLS), the base station (BS) is equipped with multiple antennas and artificial noise (AN) is injected by the BS to impair the eavesdroppers' channels. To meet the stringent delay requirements in secure URLLC systems, short packet transmission (SPT) is adopted and taken into consideration for resource allocation design. The resource allocation algorithm design is formulated as an optimization problem for minimization of the total transmit power, while guaranteeing quality-of-service (QoS) constraints regarding the URLLC users' number of transmitted bits, packet error probability, information leakage, and delay. Due to the non-convexity of the optimization problem, finding a global solution entails a high computational complexity. Thus, we propose a low-complexity algorithm based successive convex approximation (SCA) to find a sub-optimal solution. Our simulation results show that the proposed resource allocation algorithm design ensures the secrecy of the URLLC users' transmissions, and yields significant power savings compared to a baseline scheme.