Plant height is an important agronomic trait with a significant impact on grain yield, as demonstrated by the positive effect of the REDUCED HEIGHT (RHT) dwarfing alleles (Rht1b) on lodging and harvest index in the "Green Revolution" wheat varieties. However, these gibberellic acid (GA)-insensitive alleles also reduce coleoptile length, biomass production, and yield potential in some environments, triggering the search for alternative GA-sensitive dwarfing genes. Here we report the identification, validation, and characterization of the gene underlying the GA-sensitive dwarfing locus RHT25 in wheat. This gene, designated as PLATZ-A1 (TraesCS6A02G156600), is expressed mainly in the elongating stem and developing spike and encodes a plant-specific AT-rich sequence- and zinc-binding protein (PLATZ). Natural and induced loss-of-function mutations in PLATZ-A1 reduce plant height and its overexpression increases plant height, demonstrating that PLATZ-A1 is the causative gene of RHT25. PLATZ-A1 and RHT1 show a significant genetic interaction on plant height, and their encoded proteins interact with each other in yeast and wheat protoplasts. These results suggest that PLATZ1 can modulate the effect of DELLA on wheat plant height. We identified four natural truncation mutations and one promoter insertion in PLATZ-A1 that are more frequent in modern varieties than in landraces, suggesting positive selection during wheat breeding. These mutations can be used to fine-tune wheat plant height and, in combination with other GA-sensitive dwarfing genes, to replace the GA-insensitive Rht1b alleles and search for grain yield improvements beyond those of the Green Revolution varieties.