In the presence of Gaussian noise and low-rank, partly homogenous clutter, detectors based on the full-rank assumption lose the constant false alarm rate (CFAR) property, while those relying on clutter nulling perform poorly for targets within the clutter subspace. This paper addresses the CFAR detection problem of Doppler distributed targets via invariance theory. Assuming the target lies in the target subspace, its detection problem is transformed into a canonical form by both the clutter and target subspaces. Then, the maximal invariant statistics and the conditions for CFAR detection are derived via invariance theory. Following this framework, the generalized likelihood ratio test is decomposed to obtain two CFAR components for the clutter subspace echo and the noise subspace echo. When the clutter subspace is known, a CFAR detector is constructed by combining the two components with the weight that maximizes detection probability. With unknown clutter subspace, the test is further generalized into an asymptotic CFAR detector based on the clutter subspace estimate and the asymptotic distribution of the estimate. The CFAR properties and detection performances of these detectors are validated through simulations and measured clutter.