We present a non-invasive method based on Optical Coherence Elastography (OCE) enabling the in vivo segmentation of morphological tissue constituents, in particular, monitoring of morphological alterations during both tumor development and its response to therapies. The method uses compressional OCE to reconstruct tissue stiffness map as the first step. Then the OCE-image is divided into regions, for which the Young's modulus (stiffness) falls in specific ranges corresponding to the morphological constituents to be discriminated. These stiffness ranges (characteristic "stiffness spectra") are initially determined by careful comparison of the "goldstandard" histological data and the OCE-based stiffness map for the corresponding tissue regions. After such precalibration, the results of morphological segmentation of OCE-images demonstrate a striking correlation with the histological results in terms of percentage of the segmented zones. To demonstrate high sensitivity of the OCEmethod and its excellent correlation with conventional histological segmentation we present results obtained in vivo on a murine model of breast cancer in comparative experimental study of the efficacy of two anti-tumor chemotherapeutic drugs with different mechanisms of action. The new technique allowed in vivo monitoring and quantitative segmentation of (i) viable, (ii) dystrophic, (iii) necrotic tumor cells and (iv) edema zones very similar to morphological segmentation of histological images. Numerous applications in other experimental/clinical areas requiring rapid, nearly real-time, quantitative assessment of tissue structure can be foreseen.