We study the gauge boson propagator in the dual Abelian Higgs theory which
confines electric charges. The confinement is due to dual Abrikosov-Nielsen
-Olesen strings. We show that the infrared double pole 1/(p(2))(2) in the p
ropagator is absent due to the confinement phenomenon. This result is in a
qualitative agreement with lattice numerical calculations.