Language-instructed active object localization is a critical challenge for robots, requiring efficient exploration of partially observable environments. However, state-of-the-art approaches either struggle to generalize beyond demonstration datasets (e.g., imitation learning methods) or fail to generate physically grounded actions (e.g., VLMs). To address these limitations, we introduce WoMAP (World Models for Active Perception): a recipe for training open-vocabulary object localization policies that: (i) uses a Gaussian Splatting-based real-to-sim-to-real pipeline for scalable data generation without the need for expert demonstrations, (ii) distills dense rewards signals from open-vocabulary object detectors, and (iii) leverages a latent world model for dynamics and rewards prediction to ground high-level action proposals at inference time. Rigorous simulation and hardware experiments demonstrate WoMAP's superior performance in a broad range of zero-shot object localization tasks, with more than 9x and 2x higher success rates compared to VLM and diffusion policy baselines, respectively. Further, we show that WoMAP achieves strong generalization and sim-to-real transfer on a TidyBot.