Various incremental learning (IL) approaches have been proposed to help deep learning models learn new tasks/classes continuously without forgetting what was learned previously (i.e., avoid catastrophic forgetting). With the growing number of deployed audio sensing applications that need to dynamically incorporate new tasks and changing input distribution from users, the ability of IL on-device becomes essential for both efficiency and user privacy. However, prior works suffer from high computational costs and storage demands which hinders the deployment of IL on-device. In this work, to overcome these limitations, we develop an end-to-end and on-device IL framework, FastICARL, that incorporates an exemplar-based IL and quantization in the context of audio-based applications. We first employ k-nearest-neighbor to reduce the latency of IL. Then, we jointly utilize a quantization technique to decrease the storage requirements of IL. We implement FastICARL on two types of mobile devices and demonstrate that FastICARL remarkably decreases the IL time up to 78-92% and the storage requirements by 2-4 times without sacrificing its performance. FastICARL enables complete on-device IL, ensuring user privacy as the user data does not need to leave the device.