  Recently, the XENON1T collaboration reported an excess in the electron recoil
energy spectrum. One of the simplest new physics interpretation is a new
neutrino-electron interaction mediated by a light vector particle. However, for
the parameter region favored by this excess, the constraints from the stellar
cooling are severe. Still, there are astrophysical uncertainties on those
constraints. In this paper, we discuss the constraint on the light mediator
from the effective number of neutrino Neff in the CMB era, which provides an
independent constraint. We show that Neff is significantly enhanced and exceeds
the current constraint in the parameter region favored for the XENON1T excess.
As a result, the interpretation by a light mediator heavier than about 1 eV is
excluded by the Neff constraint.
