We study the possibility of probing different texture zero neutrino mass matrices at long baseline neutrino experiment DUNE. Assuming a diagonal charged lepton basis and Majorana nature of light neutrinos, we first classify the possible light neutrino mass matrices with one and two texture zeros and then numerically evaluate the parameter space in terms of atmospheric mixing angle $theta_{23}$ and Dirac CP phase $delta_{text{CP}}$ which satisfies the texture zero conditions. We then feed these parameter values into the numerical analysis in order to study the sensitivity of DUNE experiment to them. We find that the DUNE will be able to exclude some of these texture zero mass matrices which restrict the $(theta_{23}-delta_{text{CP}})$ to a very specific range of values.