We present the results from deep X-ray observations (~400 ks in total) of SN 1006 by the X-ray astronomy satellite Suzaku. The thermal spectrum from the entire supernova remnant (SNR) exhibits prominent emission lines of O, Ne, Mg, Si, S, Ar, Ca, and Fe. The observed abundance pattern in the ejecta components is in good agreement with that predicted by a standard model of Type Ia supernovae (SNe). The spatially resolved analysis reveals that the distribution of the O-burning and incomplete Si-burning products (Si, S, and Ar) is asymmetric, while that of the C-burning products (O, Ne, and Mg) is relatively uniform in the SNR interior. The peak position of the former is clearly shifted by 5 (~3.2 pc at a distance of 2.2 kpc) to the southeast from the SNRs geometric center. Using the SNR age of ~1000 yr, we constrain the velocity asymmetry (in projection) of ejecta to be ~3100 km/s. The abundance of Fe is also significantly higher in the southeast region than in the northwest region. Given that the non-uniformity is observed only among the heavier elements (Si through Fe), we argue that SN 1006 originates from an asymmetric explosion, as is expected from recent multi-dimensional simulations of Type Ia SNe, although we cannot eliminate the possibility that an inhomogeneous ambient medium induced the apparent non-uniformity. Possible evidence for the Cr K-shell line and line broadening in the Fe K-shell emission is also found.