Since Chen et al. reported on the photonic nanojet (PNJ), many researches have been carried out from various viewpoints such as fundamental physics and device applications. We have numerically analyzed, based on the finite-difference time-domain (FDTD) method, generation of PNJ from microcylinders incorporating the liquid crystals (LCs) with radial hedgehog and tangential alignments, in which the director of LC molecules is perpendicular or parallel to the LC/matrix interface. For the radial hedgehog alignment of LC molecules, the PNJ from LC microcylinders is separated into two beams. For the tangential alignment of LC molecules, we show that the PNJ from LC microcylinders are uniquely polarized reflecting birefringence of LCs, which cannot be obtained using optically isotropic microdroplets or microcylinders. By using the LC micro-systems, we may obtain a rich variety of PNJ with electrical tunability.