  In this paper, I study spherically symmetric solutions in a simple class of
geometric sigma models of the Universe. This class of models is a subclass of
the wider class of scalar-tensor theories of gravity. The purpose of this work
is to examine how the additional scalar degree of freedom modifies Newtonian
gravitational force. The general solution for spherically symmetric metric far
from the point source is obtained in a weak field approximation. As it turns
out, it is parametrized by the mass of the source, and an additional function
of time. One particular model is examined as an example. It is shown that there
are solutions that accommodate MOND regime at some distances from the source.
Unfortunately, the obtained interval of distances turns out to be smaller than
it is needed. An additional analysis shows that genuine MOND, that explains
galactic curves of all nearby galaxies, cannot be obtained.
