Process reward models (PRMs) have shown success in complex reasoning tasks for large language models (LLMs). However, their application to machine translation (MT) remains underexplored due to the lack of systematic methodologies and evaluation benchmarks. To address this gap, we introduce \textbf{MT-RewardTree}, a comprehensive framework for constructing, evaluating, and deploying process reward models in MT. Unlike traditional vanilla preference pair construction, we propose a novel method for automatically generating token-level preference pairs using approximate Monte Carlo Tree Search (MCTS), which mitigates the prohibitive cost of human annotation for fine-grained steps. Then, we establish the first MT-specific reward model benchmark and provide a systematic comparison of different reward modeling architectures, revealing that token-level supervision effectively captures fine-grained preferences. Experimental results demonstrate that our MT-PRM-Qwen-2.5-3B achieves state-of-the-art performance in both token-level and sequence-level evaluation given the same input prefix. Furthermore, we showcase practical applications where PRMs enable test-time alignment for LLMs without additional alignment training and significantly improve performance in hypothesis ensembling. Our work provides valuable insights into the role of reward models in MT research. Our code and data are released in \href{https://sabijun.github.io/MT_RewardTreePage/}{https://sabijun.github.io/MT\_RewardTreePage}.