Stain normalization of microscopic images is the first pre-processing step in any computer-assisted automated diagnostic tool. This paper proposes Geometry-inspired Chemical-invariant and Tissue Invariant Stain Normalization method, namely GCTI-SN, for microscopic medical images. The proposed GCTI-SN method corrects for illumination variation, stain chemical, and stain quantity variation in a unified framework by exploiting the underlying color vector space’s geometry. While existing stain normalization methods have demonstrated their results on a single tissue and stain type, GCTI-SN is benchmarked on three cancer datasets of three cell/tissue types prepared with two different stain chemicals. GCTI-SN method is also benchmarked against the existing methods via quantitative and qualitative results, validating its robustness for stain chemical and cell/tissue type. Further, the utility and the efficacy of the proposed GCTI-SN stain normalization method is demonstrated diagnostically in the application of breast cancer detection via a CNN-based classifier.