  Using $e^{+}e^{-}$ collision data collected with the BESIII detector at the
BEPCII collider corresponding to an integrated luminosity of 5.2 $fb^{-1}$ at
center-of-mass energies ($\sqrt{s}$) from 4.009 to 4.600 GeV, the process
$e^{+}e^{-} \to \pi^{0} \pi^{0}\psi(3686)$ is studied for the first time. The
corresponding Born cross sections are measured and found to be half of those of
the reaction $e^{+}e^{-} \to \pi^{+}\pi^{-}\psi(3686)$. This is consistent with
the expectation from isospin symmetry. Furthermore, the Dalitz plots for
$\pi^{0}\pi^{0}\psi(3686)$ are accordant with those of
$\pi^{+}\pi^{-}\psi(3686)$ at all energy points, and a neutral analogue to the
structure in $\pi^\pm \psi(3686)$ around 4040 MeV/$c^{2}$ first observed at
$\sqrt{s}$=4.416 GeV is observed in the isospin neutral mode at the same
energy.
