  We modify the calculation of quarkonium masses using the radial WKB and
Pekeris-type approximations for the case of three-dimensional, rotationally
invariant non-commutative space. We obtain corrections to the charmonium
($\text{c}\bar{\text{c}}$), bottomonium ($\text{b}\bar{\text{b}}$) and
bottom-charmed meson ($\text{c}\bar{\text{b}}$) masses due to the discrete
short distance structure of the space introduced by the space
non-commutativity. For the fundamental length at the Planck scale we obtain
relative correction at the order of $10^{-39}$, and taking into account the
current experimental data, we obtain the upper bound at the order of
${10^{-18}\textrm{ m}}$ for the fundamental length scale of space.
