Accurate mapping of irrigation methods is crucial for sustainable agricultural practices and food systems. However, existing models that rely solely on spectral features from satellite imagery are ineffective due to the complexity of agricultural landscapes and limited training data, making this a challenging problem. We present Knowledge-Informed Irrigation Mapping (KIIM), a novel Swin-Transformer based approach that uses (i) a specialized projection matrix to encode crop to irrigation probability, (ii) a spatial attention map to identify agricultural lands from non-agricultural lands, (iii) bi-directional cross-attention to focus complementary information from different modalities, and (iv) a weighted ensemble for combining predictions from images and crop information. Our experimentation on five states in the US shows up to 22.9\% (IoU) improvement over baseline with a 71.4% (IoU) improvement for hard-to-classify drip irrigation. In addition, we propose a two-phase transfer learning approach to enhance cross-state irrigation mapping, achieving a 51% IoU boost in a state with limited labeled data. The ability to achieve baseline performance with only 40% of the training data highlights its efficiency, reducing the dependency on extensive manual labeling efforts and making large-scale, automated irrigation mapping more feasible and cost-effective.