In this paper, a new framework for tensor hyperspectral target detection is proposed. In this new framework, tensor is well integrated into the conventional target detection algorithm. As a result, a tensor matched subspace detector (MSD) for hyperspectral target detection is proposed. The proposed method is mainly applied to detect multipixel targets rather than subpixel targets. In this new method, the hyperspectral data are considered as a form of third-order tensor in order to jointly utilize the information of multidimensional data. In conventional detection methods, the spatial-spectral information has not been taken into account, even some algorithms have been presented for improving the utilization efficiency of the spatial-spectral structural feature, but the overall structural characteristic of the extracted feature is still ignored. In our algorithm, the tensor subspace projection is defined for the first time, which is easily calculated by three predetermined orthogonal direction mapping matrices without any iteration. Then, the test tensor blocks are projected into the tensor subspace and finally measured by the ratio of residual energy, just like the general likelihood ratio test. The proposed method can be regarded as an extension of conventional MSD. The reliability and superiority are demonstrated by the experiments on real hyperspectral imaging data sets. The experimental results indicate that our approach compares favorably to some classical and novel methods by jointly processing multidimensional data with tensorial form.