We present the results of extinction measurements toward the main ejecta shell of the Cassiopeia A supernova (SN) remnant using the flux ratios between the two near-infrared (NIR) [Fe II] lines at 1.26 and 1.64 $mu {rm m}$. We find a clear correlation between the NIR extinction ($E(J-H)$) and the radial velocity of ejecta knots, showing that redshifted knots are systematically more obscured than blueshifted ones. This internal self-extinction strongly indicates that a large amount of SN dust resides inside and around the main ejecta shell. At one location in the southern part of the shell, we measure $E(J-H)$ by the SN dust of 0.23$pm$0.05 mag. By analyzing the spectral energy distribution of thermal dust emission at that location, we show that there are warm ($sim$100 K) and cool ($sim$40 K) SN dust components and that the latter is responsible for the observed $E(J-H)$. We investigate the possible grain species and size of each component and find that the warm SN dust needs to be silicate grains such as MgSiO$_{3}$, Mg$_{2}$SiO$_{4}$, and SiO$_{2}$, whereas the cool dust could be either small ($leq$0.01 $mu {rm m}$) Fe or large ($geq$0.1 $mu {rm m}$) Si grains. We suggest that the warm and cool dust components in Cassiopeia A represent grain species produced in diffuse SN ejecta and in dense ejecta clumps, respectively.