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The paramagnetic spin-triplet superconductor candidate UTe_{2} has attracted significant attention because of its exotic superconducting properties including an extremely high upper critical field and possible chiral superconducting states. Recently, ultraclean single crystals of UTe_{2} have become available, and thus measurements on these crystals are crucial to elucidate the intrinsic superconducting properties. Here, we report the thermodynamic critical field H_{c}, the lower critical field H_{c1}, and the upper critical field H_{c2} at low fields of these high-quality single crystals. From the comparison of the anisotropies in H_{c1} and H_{c2}, we find that the experimental H_{c1} values with the magnetic field along the b and c axes are anomalously enhanced, showing unusual low-temperature upturns. We propose an effect of the strong Ising-like ferromagnetic fluctuations on the vortex line energy as the origin of the anisotropic enhancement of H_{c1}.