Neural Inertial Navigation (NIN) plays a pivotal role in self-localization, aiming to infer the position of a mobile entity using noisy data from the onboard inertial measurement unit (IMU). Most existing methods rely on convolutional neural networks (CNNs) to capture dependencies among multiple variables, yet the time-frequency and invariant underlying features of IMU measurements remain underexplored. In this paper, we propose MInF, a Multi-Band Invariant Feature Learning for Efficient Inertial Navigation. The MInF advances mainly in two aspects. First, we design a Wavelet-based Multi-Band Mixer (MBMixer) for neural inertial navigation, which leverages the merits of multi-band 1D wavelet decomposition and Multi-Layer Perceptron (MLP)-based mixing to efficiently extract information in both the time and frequency domains in IMU measurements. Second, we introduce a self-supervised learning (SSL) method for learning invariant underlying features from inertial data without the need for any semantic labels. On the one hand, we learn a multi-task MBMixer via jointly classifying different transformations (i.e., pretext tasks) applied to an input signal for extracting invariant underlying features. On the other hand, we use the learned MBMixer in pretext task as the pre-trained model and fine-tune it to regress velocity in the neural inertial navigation (i.e., downstream task). Extensive experiments conducted on two real-world datasets demonstrate that the proposed MInF achieves SOTA results in neural inertial navigation, leading to 15% performance improvement while maintaining a low memory footprint and computational cost.