We present magnetotransport studies on a series of BaFe2−xNixAs2 (0.03 ≤ x ≤ 0.10) single crystals. In the underdoped (x = 0.03) non-superconducting sample, the temperature-dependent resistivity exhibits a peak at 22 K, which is associated with the onset of filamentary superconductivity (FLSC). FLSC is suppressed by an external magnetic field in a manner similar to the suppression of bulk superconductivity in an optimally-doped (x = 0.10) compound, suggesting the same possible origin as the bulk superconductivity. Our magnetoresistivity measurements reveal that FLSC persists up to the optimal doping and disappears in the overdoped regime where the long-range antiferromagnetic order is completely suppressed, pointing to a close relation between FLSC and the magnetic order.