We present evidence for the exotic charged charmonium-like state $Z_c^{\pm}(3900)$ in semi-inclusive weak decays of $b$-flavored hadrons. The signal is correlated with a $J/\psi \pi^+ \pi^-$ system in the invariant mass range 4.2$-$4.7~GeV and includes the sequential process $b$-quark hadron $ \rightarrow Y(4260) +$ anything, $Y(4260) \rightarrow Z_c^{\pm}(3900) \pi^{\mp}$, $Z_c^{\pm}(3900) \rightarrow J/\psi \pi^{\pm}$. The study is based on $10.4~\rm{fb^{-1}}$ of $p \overline p $ collision data collected by the D0 experiment at the Fermilab Tevatron collider.