We study the phenomenology of two-zero textures of $M_{\nu }^{4\times 4}$ neutrino mass matrices in the minimal extended seesaw (MES) mechanism. $M_{\nu }^{4\times 4}$ involves $3\times 3$ Dirac neutrino mass matrix ($M_D$), $3\times 3$ right-handed Majorana neutrino mass matrix $M_R$ and $1\times 3$ matrix $M_S$ that couples the singlet field ‘S’ with the right-handed neutrinos. We consider the phenomenologically predictive cases (5+3) and (6+2) schemes for zero textures of $M_D$ and $M_R$ of $3\times 3$ active sector of $M_{\nu }^{4\times 4}$ along with admissible one or two-zero textures of $M_S$. Although there is a large number of combinations of $M_D,M_R$ and $M_S$ leading to the desired two-zero textures, $S_3$ group transformations between the different zero textures of $M_D,M_R$ and $M_S$ reduce them to a small number of basic combinations. In MES, $M_{\nu }^{4\times 4}$ should be a matrix of rank 3, so we have 12 two-zero textures of neutrino mass matrices of rank 3 out of total 15 two-zero textures of neutrino mass matrices. In realization of the two-zero textures in (5+3) scheme we have obtained a number of correlations among the neutrino mass matrix elements $m_{ij}$, while none of the two-zero textures could be realized in the (6+2) scheme. The viability of each of the realizable textures is checked by plotting the scatter plots of their respective correlations under the current neutrino oscillation data. We have analysed the role played by the Dirac and Majorana CP phases for each of the textures. For constrained ranges of CP phases we also draw scatter plots for Jarlskog invariant ($J_{CP}$) and effective electron neutrino mass $\left|m_{\beta \beta }\right|$. In our study the viable textures are finally realized by $Z_8$ Abelian group symmetry by extending the Standard Model to include few scalar fields.