We investigate whether the spin or charge degrees of freedom are responsible for the nodal gap in underdoped cuprates by performing inelastic neutron scattering and x-ray diffraction measurements on La_2-xSr_xCuO₄, which is on the edge of the antiferromagnetic phase. We found that a fluctuating incommensurate spin-density wave (SDW) with a bottom part of an hourglass dispersion exists even in this magnetic sample. The strongest component of these fluctuations diminishes at the same temperature where the nodal gap opens. X-ray scattering measurements on the same crystal show no signature of a charge-density wave (CDW). Therefore, we suggest that the nodal gap in the electronic band of this cuprate opens due to fluctuating SDW with no contribution from CDW.