  A canonical quantization \`a la Wheeler-DeWitt is performed for a model of
three-form fields in a homogeneous and isotropic universe. We start by carrying
out the Hamiltonian formalism of this cosmological model. We then apply this
formalism to a Little Sibling of the Big Rip (LSBR), an abrupt event milder
than a Big Rip and that is known to be generic to several minimally coupled
three-form fields for a variety of potentials. We obtain a set of analytical
solutions of the Wheeler-DeWitt equation using different analytical
approximations and explore the physical consequences of them. It turns out that
there are quantum states where the wave function of the universe vanishes, i.e.
the DeWitt condition is fulfilled for them. Given that this happens only for
some subset of solutions of the Wheeler-DeWitt equation, this points out that
the matter inducing the LSBR is equally important in the process as, it has
been previously shown, a minimally coupled phantom scalar field feeding
classically a LSBR is smoothed at the quantum level, i.e. all the quantum
states lead to a vanishing wave function.
