IC 443 is famous for its interaction with nearby molecular clouds and intense H2 emission lines in infrared. Therefore, it has been studied extensively for the understanding of molecular shocks. We observed H2 mission lines toward the shock-cloud interaction regions of IC 443, known as clumps B, C, and G. The observations were performed with the InfraRed Camera (IRC) onboard a satellite AKARI over 2.5-5.0 um, where previous space observations, e.g. Infrared Space Observatory (ISO) and Spitzer, do not cover. Our AKARI observations provide spectra of sequential pure-rotational and ro-vibrational H2 emission lines. For the clumps C and G, combining with previous mid-infrared observational results, we found that the H2 level populations show a significant separation between v=0 and v=1 levels; v=1 levels are under-populated than v=0 levels, therefore, the population cannot be described by two temperature LTE model, as many people have analyzed for the shocked H2 gas. We also applied the thermal admixture model, dN(H2; T)~T^(-b) dT, with varying ortho-to-para ratios according to the temperature, to describe the level population, and obtained plausible ranges of the H2 gas density and power-law index b.