Detecting large-scale structures in the intergalactic medium (IGM) during cosmic reionization via absorption of 21 cm spectral line of neutral Hydrogen against a background radiation is a powerful and independent technique complementary to the three-dimensional tomography and power spectrum techniques. The direct detection of this absorption is very challenging because it requires very bright (>10–100 mJy) background sources at high redshifts (z > 8), which are evidently rare; very long times of integration; or instruments of very high sensitivity. Instead, a statistical approach is found to be significantly more viable using one-dimensional (1D) power spectrum along narrow sightlines but with fainter background objects (<1–10 mJy), which are likely to be more abundant and significant contributors at high redshifts. This approach reduces cosmic variance and improves sensitivity especially on small spatial scales. The prospects of detecting the 1D power spectrum of the IGM along selected narrow directions are investigated against uncertainties from thermal noise and the chromatic synthesized point spread function (PSF) response. Minimum requirements on the number of high-redshift background sources, the telescope sensitivity, and the PSF quality are estimated for a range of instrumental, background source, and reionization model parameters. A 1000-hour observing campaign with modern radio telescopes, especially the Square Kilometre Array, can detect the 1D power spectrum on a range of spatial scales and redshifts, and potentially discriminate between models of cosmic reionization.