In this paper, we construct a framework of the movable antenna (MA) aided covert communication shielded by the general noise uncertainty for the first time. According to the analysis performance on the derived closed-form expressions of the sum of the probabilities of the detection errors and the communication outage probability, the perfect covertness and the ultra reliability can be achieved by adjusting the antenna position in the MA array. Then, we formulate the communication covertness maximization problem with the constraints of the ultra reliability and the independent discrete movable position to optimize the transmitter's parameter. With the maximal ratio transmitting (MRT) design for the beamforming, we solve the closed-form optimal information transmit power and design a lightweight discrete projected gradient descent (DPGD) algorithm to determine the optimal antenna position. The numerical results show that the optimal achievable covertness and the feasible region of the steering angle with the MA array is significant larger than the one with the fixed-position antenna (FPA) array.