  We analyze the adiabatic regularization scheme to renormalize Proca fields in
a four-dimensional Friedmann-Lema\^{i}tre-Robertson-Walker spacetime. The
adiabatic method is well established for scalar and spin-$1/2$ fields, but is
not yet fully understood for spin-$1$ fields. We give the details of the
construction and show that, in the massless limit, the renormalized
stress-energy tensor of the Proca field is closely related to that of a
minimally coupled scalar field. Our result is in full agreement with other
approaches, based on the effective action, which also show a discontinuity in
the massless limit. The scalar field can be naturally regarded as a
St\"ueckelberg-type field. We also test the consistency of our results in de
Sitter space.
