Medical hyperspectral imagery has recently attracted considerable attention. However, for identification tasks, the high dimensionality of hyperspectral images usually leads to poor performance. Thus, dimensionality reduction (DR) is crucial in hyperspectral image analysis. Motivated by exploiting the underlying structure information of medical hyperspectral images and enhancing the discriminant ability of features, a discriminant tensor-based manifold embedding (DTME) is proposed for discriminant analysis of medical hyperspectral images. Based on the idea of manifold learning, a new discriminant similarity metric is designed, which takes into account the tensor representation, sparsity, low-rank and distribution characteristics. Then, an inter-class tensor graph and an intra-class tensor graph are constructed using the new similarity metric to reveal intrinsic manifold of hyperspectral data. Dimensionality reduction is achieved by embedding this supervised tensor graphs into the low-dimensional tensor subspace. Experimental results on membranous nephropathy and white bloodcells identification tasks demonstrate the potential clinical value of the proposed DTME.