Metallized film capacitors (MFCs) have been widely used in power electronics such as DC transmission, electric vehicles, and wind power converters, due to their high reliability. MFCs have the unique self-healing discharge characteristics, which can eliminate internal defects and achieve stable operation. The self-healing discharge signal, which correlates with the degradation of MFCs, can be utilized as a characteristic parameter for assessment. In this paper, an intelligent monitoring approach for assessing the degradation status of MFCs based on the ultrasonic eigenfrequency of self-healing discharge signals is proposed. 1D-convolutional neural network (1D-CNN) is used for feature extraction and classification. The experimental results reveal that the method can quickly extract the ultrasonic eigenfrequency feature of a period of time, and the accuracy of degradation status classification reaches 98.1%, showing superior performance in degradation status of MFCs monitoring conditions.