We present OuroMamba, the first data-free post-training quantization (DFQ) method for vision Mamba-based models (VMMs). We identify two key challenges in enabling DFQ for VMMs, (1) VMM's recurrent state transitions restricts the capturing of long-range interactions and leads to semantically weak synthetic data, (2) VMM activations exhibit dynamic outlier variations across time-steps, rendering existing static PTQ techniques ineffective. To address these challenges, OuroMamba presents a twostage framework: (1) OuroMamba-Gen to generate semantically rich and meaningful synthetic data. It applies contrastive learning on patch level VMM features generated through neighborhood interactions in the latent state space, (2) OuroMamba-Quant to employ mixedprecision quantization with lightweight dynamic outlier detection. In specific, we present a thresholding based outlier channel selection strategy for activations that is updated every time-step. Extensive experiments across vision and generative tasks show that our data-free OuroMamba surpasses existing data-driven $P T Q$ techniques, achieving state-of-the-art performance across diverse quantization settings. Additionally, we implement efficient GPU kernels to achieve practical latency speedup of up to $\mathbf{2. 3 6} \times$. Code and synthetic dataset are available here: https://github.com/georgia-tech-synergy-lab/ICCV-OuroMamba.