Short-term precipitation nowcasting is an inherently uncertain and under-constrained spatiotemporal forecasting problem, especially for rapidly evolving and extreme weather events. Existing generative approaches rely primarily on visual conditioning, leaving future motion weakly constrained and ambiguous. We propose a language-aware multimodal nowcasting framework(LangPrecip) that treats meteorological text as a semantic motion constraint on precipitation evolution. By formulating nowcasting as a semantically constrained trajectory generation problem under the Rectified Flow paradigm, our method enables efficient and physically consistent integration of textual and radar information in latent space.We further introduce LangPrecip-160k, a large-scale multimodal dataset with 160k paired radar sequences and motion descriptions. Experiments on Swedish and MRMS datasets show consistent improvements over state-of-the-art methods, achieving over 60 \% and 19\% gains in heavy-rainfall CSI at an 80-minute lead time.