Two-dimensional (2D) kagome metals offer a unique platform for exploring electron correlation phenomena derived from quantum many-body effects. Here, we report a combined study of electrical magnetotransport and neutron scattering on YbFe₆Ge₆, where the Fe moments in the 2D kagome layers exhibit an A-type collinear antiferromagnetic order below T_N≈500 K. Interactions between the Fe ions in the layers and the localized Yb magnetic ions in between reorient the c-axis-aligned Fe moments to the kagome plane below T_SR≈63 K. Our magnetotransport measurements show an intriguing anomalous Hall effect (AHE) that emerges in the spin-reorientated collinear state, accompanied by the closing of the spin anisotropy gap as revealed from inelastic neutron scattering. The gapless spin excitations and the Yb-Fe interaction are able to support a dynamic scalar spin chirality, which explains the observed AHE. Therefore, our Letter demonstrates that spin fluctuations may provide an additional scattering channel for the conduction electrons and give rise to AHE even in a collinear antiferromagnet.