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Keyword spotting (KWS) is a key technology in smart devices. However, privacy issues in these devices have been constantly raised. To solve this problem, this paper applies homomorphic encryption (HE) to a previous small-footprint convolutional neural network (CNN)-based KWS algorithm. This allows for a trustless system in which a command word can be securely identified by a remote cloud server without exposing client data. To alleviate the burden on an edge device of a client, a novel packing technique is proposed that reduces the number of ciphertexts for an input keyword to one. Our HE-based KWS shows a prediction accuracy of 72% for Google's Speech Commands Dataset with 12 labels. This is almost identical to the accuracy of the non-HE-based implementation that has the same CNN layers and approximates a rectified linear unit in the same manner. On a workstation, it takes 19 seconds to process one keyword on average, which can be improved in the future through parallelization, HE parameter optimization, and/or the use of custom hardware accelerators.