Traditional drone-view geo-localization (DVGL) methods based on artificial neural networks (ANNs) have achieved remarkable performance. However, ANNs rely on dense computation, which results in high power consumption. In contrast, spiking neural networks (SNNs), which benefit from spike-driven computation, inherently provide low power consumption. Regrettably, the potential of SNNs for DVGL has yet to be thoroughly investigated. Meanwhile, the inherent sparsity of spike-driven computation for representation learning scenarios also results in loss of critical information and difficulties in learning long-range dependencies when aligning heterogeneous visual data sources. To address these, we propose SpikeViMFormer, the first SNN framework designed for DVGL. In this framework, a lightweight spike-driven transformer backbone is adopted to extract coarse-grained features. To mitigate the loss of critical information, the spike-driven selective attention (SSA) block is designed, which uses a spike-driven gating mechanism to achieve selective feature enhancement and highlight discriminative regions. Furthermore, a spike-driven hybrid state space (SHS) block is introduced to learn long-range dependencies using a hybrid state space. Moreover, only the backbone is utilized during the inference stage to reduce computational cost. To ensure backbone effectiveness, a novel hierarchical re-ranking alignment learning (HRAL) strategy is proposed. It refines features via neighborhood re-ranking and maintains cross-batch consistency to directly optimize the backbone. Experimental results demonstrate that SpikeViMFormer outperforms state-of-the-art SNNs. Compared with advanced ANNs, it also achieves competitive performance.Our code is available at https://github.com/ISChenawei/SpikeViMFormer