Dense gas in minihalos (MHs) with masses of $10^6-10^8~M_\odot$ can shield themselves from reionization for about $100$ megayears after being exposed to UV radiation. These self-shielded systems, often unresolved in cosmological simulations, can introduce strong absorption in quasar spectra. This paper is the first systematic study on the impact of these systems on the Ly$\alpha$ forest. We first derive the HI column density profile of photoevaporating MHs by conducting 1-dimensional radiation-hydrodynamics simulations. We utilize these results to estimate the Ly$\alpha$ opacity from minihalos in a large-scale simulation that cannot resolve the self-shielding process. When the ionization rate of the background radiation is $0.03\times 10^{-12}~{\rm s}^{-1}$, as expected near the end of reionization at $z\sim 5.5$, we find that the incidence rate of damped Ly$\alpha$ absorbers, $dN/dX$, increases by nearly a factor of 2 - 4 compared to at $z=4.5$. The Ly$\alpha$ flux is, on average, suppressed by $10\%$ of its mean due to absorption by MHs. The extended absorption features contribute to a $\sim 20\%$ enhancement in the 1D power spectrum at $k\sim 0.1~h~{\rm Mpc}^{-1}$ ($10^{-3}~{\rm km}^{-1}~{\rm s}$), which is comparable to the enhancement caused by inhomogeneous reionization. Notably, the flux is particularly suppressed in the vicinity of large halos along the line-of-sight direction at separations of up to $10~h^{-1}~{\rm Mpc}$ at $r_\perp\lesssim 2~h^{-1}~{\rm Mpc}$. However, these effects become much smaller for higher ionizing rates ($0.3$ and $1\times 10^{-12}~{\rm s}^{-1}$) expected in the post-reionization universe $z\lesssim5.5$. Our findings highlight the need to consider the absorption by MHs when interpreting the Ly$\alpha$ forest at $z\gtrsim5.5$. Moreover, the sensitivity of this effect to the ionizing background intensity can be exploited to constrain the intensity itself.
Comment: 15 pages; 11 figures; Submitted to the ApJ