In this study, we propose using an over-the-air computation (OAC) scheme for the federated k-means clustering algorithm to reduce the per-round communication latency when it is implemented over a wireless network. The OAC scheme relies on an encoder exploiting the representation of a number in a balanced number system and computes the sum of the updates for the federated k-means via signal superposition property of wireless multiple-access channels non-coherently to eliminate the need for precise phase and time synchronization. Also, a reinitialization method for ineffectively used centroids is proposed to improve the performance of the proposed method for heterogeneous data distribution. For a customer-location clustering scenario, we demonstrate the performance of the proposed algorithm and compare it with the standard k-means clustering. Our results show that the proposed approach performs similarly to the standard k-means while reducing communication latency.