Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of interfacial viscous shear forces due to flow in the viscous matrix. A representative axial nematic orientation texture is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wavenumber m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, including the orientation contribution to the surface elasticity and surface bending stresses. Surface gradients of bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic orientation and the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric, with finite or unbounded wavelengths. Thus, the classical fiber-to-droplet transformation is one of several possible instability pathways while others include surface fibrillation. The contribution of the viscosity ratio to the capillary instabilities of a thin nematic fiber in a viscous matrix is analyzed by two parameters, the fiber and matrix Ohnesorge numbers, which represent the ratio between viscous and surface forces in each phase. The capillary instabilities of a thin nematic fiber in a viscous matrix are suppressed by increasing either the fiber or matrix Ohnesorge number, but estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing matrix Ohnesorge number.