  We investigate the interactions of the charged exotic state $Z_c(3900)$ in a
hadronic medium composed of light mesons. We study processes such as $Z_c \pi
\to D\bar{D}$, $Z_c \pi \to D^*\bar{D}^*$, $Z_c \pi \to D\bar{D}^*$ and the
inverse ones. Using effective Lagrangians and form factors calculated with QCD
sum rules (treating the $Z_c(3900)$ as a tetraquark) we estimate the vacuum and
thermally-averaged cross-sections of these reactions. We find that the
$Z_c(3900)$ has relatively large interaction cross sections with the
constituent particles of the hadronic medium. After that, we use the production
and suppression cross sections in a rate equation to estimate the time
evolution of the $Z_c$ multiplicity. We include the $Z_c$ decay and
regeneration terms. The coalescence model is employed to compute the initial
$Z_c$ multiplicity for the compact tetraquark configuration. Our results
indicate that the combined effects of hadronic interactions, hydrodynamical
expansion, decay and regeneration affect the final yield, which is bigger than
the initial value. Besides, the dependence of the $Z_c$ final yield with the
centrality, center-of-mass energy and the charged hadron multiplicity measured
at midrapidity $[dN_{ch}/d\eta \,(\eta<0.5)]$ is also investigated.
