  We study the zero textures of the Yukawa matrices in the minimal extended
type-I seesaw (MES) model which can give rise to $\sim$ eV scale sterile
neutrinos. In this model, three right handed neutrinos and one extra singlet
$S$ are added to generate a light sterile neutrino. The light neutrino mass
matrix for the active neutrinos, $ m_{\nu}$, depends on the Dirac neutrino mass
matrix ($ M_{D} $), Majorana neutrino mass matrix ($ M_{R} $) and the mass
matrix ($ M_{S} $) coupling the right handed neutrinos and the singlet. The
model predicts one of the light neutrino masses to vanish. We systematically
investigate the zero textures in $ M_{D} $ and observe that maximum five zeros
in $ M_{D} $ can lead to viable zero textures in $ m_{\nu} $. For this study we
consider four different forms for $ M_R $ (one diagonal and three off diagonal)
and two different forms of $(M_{S})$ containing one zero. Remarkably we obtain
only two allowed forms of $ m_{\nu} $ ($m_{e\tau} = 0 $ and $m_{\tau\tau}=0$)
having inverted hierarchical mass spectrum. We re-analyze the phenomenological
implications of these two allowed textures of $m_\nu$ in the light of recent
neutrino oscillation data. In the context of the MES model, we also express the
low energy mass matrix, the mass of the sterile neutrino and the active-sterile
mixing in terms of the parameters of the allowed Yukawa matrices. The MES model
leads to some extra correlations which disallow some of the Yukawa textures
obtained earlier, even though they give allowed one-zero forms of $m_\nu$. We
show that the allowed textures in our study can be realized in a simple way in
a model based on MES mechanism with a discrete Abelian flavor symmetry group
$Z_8 \times Z_2$.
