  We derive a modified Buchdahl inequality for scalar-tensor theories of
gravity. In general relativity, Buchdahl has shown that the maximum value of
the mass-to-size ratio, $2M/R$, is 8/9 for static and spherically symmetric
stars under some physically reasonable assumptions. We formally apply
Buchdahl's method to scalar-tensor theories and obtain theory-independent
inequalities. After discussing the mass definition in scalar-tensor theories,
these inequalities are related to a theory-dependent maximum mass-to-size
ratio. We show that its value can exceed not only Buchdahl's limit, 8/9, but
also unity, which we call {\it the black hole limit}, in contrast to general
relativity. Next, we numerically examine the validity of the assumptions made
in deriving the inequalities and the applicability of our analytic results. We
find that the assumptions are mostly satisfied and that the mass-to-size ratio
exceeds both Buchdahl's limit and the black hole limit. However, we also find
that this ratio never exceeds Buchdahl's limit when we impose the further
condition, $\rho-3p\ge0$, on the density, $\rho$, and pressure, $p$, of the
matter.
