  We show how to realize two-zero textures of the Majorana neutrino mass matrix
$M_\nu$ based on modular $A_4$ invariant models without flavons. In these
models, all matter fields are assigned to three inequivalent singlets, ${\bf
1}$, ${\bf 1^\prime}$ and ${\bf 1^{\prime\prime}}$, of the finite modular group
$\Gamma_3 \simeq A_4$. Considering tensor products of the $A_4$ group, it is
easy to make the charged lepton mass matrix $M_\ell$ diagonal. Since not all
modular forms of a specific weight and level 3 can be arranged into three
inequivalent singlets of $A_4$ simultaneously, we can always make some entries
in $M_\nu$ vanish by properly assigning the representations and modular weights
for the matter fields. We consider two cases where neutrino masses originate
from the Weinberg operator and the type-I seesaw mechanism, respectively. For
the former case, all seven viable two-zero textures of $M_\nu$ (${\bf
A_{1,2}}$, ${\bf B_{1,2,3,4}}$ and ${\bf C}$) can be realized successfully. For
the latter case, only five of them (namely ${\bf A_{1,2}}$, ${\bf B_{3,4}}$ and
${\bf C}$) can be achieved due to the intrinsic structure of the right-handed
neutrino mass matrix $M_{\rm R}$ in our assumption for simplicity.
