  We apply the weak field approximation limit of the covariant
Scalar-Tensor-Vector Gravity (STVG) theory, so-called MOdified gravity (MOG),
to the dynamics of clusters of galaxies by using only baryonic matter. The MOG
effective gravitational potential in the weak field approximation is composed
of an attractive Newtonian term and a repulsive Yukawa term with two parameters
$\alpha$ and $\mu$. The numerical values of these parameters have been obtained
by fitting the predicted rotation curves of galaxies to observational data,
yielding the best fit result: $\alpha = 8.89 \pm 0.34$ and $\mu= 0.042\pm
0.004$ kpc$^{-1}$~\cite{rah13}. We extend the observational test of this theory
to clusters of galaxies, using data for the ionized gas and the temperature
profile of nearby clusters obtained by the Chandra X-ray telescope. Using the
MOG virial theorem for clusters, we compare the mass profiles of clusters from
observation and theory for eleven clusters. The theoretical mass profiles for
the inner parts of clusters exceed the observational data. However, the
observational data for the inner parts of clusters (i.e., $r<0.1 r_{500}$) is
scattered, but at distances larger than $\sim 300$ kpc, the observed and
predicted mass profiles converge. Our results indicate that MOG as a theory of
modified gravity is compatible with the observational data from the the solar
system to Mega parsec scales without invoking dark matter.
