We report on an infrared study of carrier dynamics within the CuO$_{2}$ planes in heavily underdoped detwinned single crystals of YBa$_{2}$Cu$_{3}$O$% _{y}$. In an effort to reveal the electronic structure near the onset of superconductivity, we investigate the strong anisotropy of the electromagnetic response due to an enhancement of the scattering rate along the a-axis. We propose that the origin of this anisotropy is related to a modulation of the electron density within the CuO$_{2}$ planes.