We have studied the total cross section, $Q^2$, momentum and angular distributions for pions in the $\nu$($\bar \nu$) induced $\pi^0$ production from nucleons. The calculations have been done for the weak production induced by the neutral current in the standard model and the electromagnetic production induced by neutrino magnetic moment. It has been found that with the present experimental limits on the muon neutrino magnetic moment $\mu_{\nu_\mu}$, the electromagnetic contribution to the cross section for the $\pi^0$ production is small. The neutrino induced neutral current production of $\pi^{0}$, while giving an alternative method to study the magnetic moment of neutrino $\mu_{\nu_\mu}$, does not provide any improvement over the present experimental limit on $\mu_{\nu_\mu}$ from the observation of this process in future experiments at T2K and NO$\nu$A.