Mixture-of-Experts (MoE) based large language models (LLMs) offer strong performance but suffer from high memory and computation costs. Weight binarization provides extreme efficiency, yet existing binary methods designed for dense LLMs struggle with MoE-specific issues, including cross-expert redundancy, task-agnostic importance estimation, and quantization-induced routing shifts. To this end, we propose MoBiE, the first binarization framework tailored for MoE-based LLMs. MoBiE is built on three core innovations: 1. using joint SVD decomposition to reduce cross-expert redundancy; 2. integrating global loss gradients into local Hessian metrics to enhance weight importance estimation; 3. introducing an error constraint guided by the input null space to mitigate routing distortion. Notably, MoBiE achieves these optimizations while incurring no additional storage overhead, striking a balance between efficiency and model performance. Extensive experiments demonstrate that MoBiE consistently outperforms state-of-the-art binary methods across multiple MoE-based LLMs and benchmarks. For example, on Qwen3-30B-A3B, MoBiE reduces perplexity by 52.2$\%$, improves average zero-shot performance by 43.4$\%$, achieves over 2 $\times$ inference speedup, and further shortens quantization time. The code is available at https://github.com/Kishon-zzx/MoBiE.