  We present both spin-independent and -dependent parts of a central interquark
potential for charmonium states, which is calculated in 2+1 flavor dynamical
lattice QCD using the PACS-CS gauge configurations with a lattice cutoff of
a^{-1}~2.2 GeV. Our simulations are performed with a relativistic heavy quark
action for the charm quark at the lightest pion mass, M_\pi=156(7) MeV, in a
spatial volume of 3fm^3. We observe that the spin-independent charmonium
potential obtained from lattice QCD with almost physical quark masses is quite
similar to the Conrnell potential used in non-relativistic potential models.
The spin-spin potential properly exhibits the short range repulsive
interaction, while its r-dependence is different from either a point-like
spin-spin potential generated by one-gluon exchange or a phenomenological
finite-range one adopted in quark potential models.
