The NA62 experiment collected a large sample of charged kaon decays in 2007 with a highly efficient trigger for decays into electrons. A measurement of the $\pi^0$ electromagnetic transition form factor slope parameter from $1.11\times10^{6}$ fully reconstructed $K^\pm \to \pi^\pm \pi^0_D, \pi^0_D \to e^+ e^-\gamma$ events is reported. The measured value $a = (3.68 \pm 0.57)\times10^{-2}$ is in good agreement with theoretical expectations and previous measurements, and represents the most precise experimental determination of the slope in the time-like momentum transfer region.