We can think of this phenomenon at molecular level.
Let's consider the acid HA, which consists of H+ and A-.
At low initial concentration, more water molecules are available for hydration of the H-A molecules, resulting in increasing ionization of the acid. But as we use more concentrated acid, the ionic interaction between the H+ and A- dominates (due to number) over the possible hydration provided by water, henceforth, the ionization decreases.
Hope my explanation helps