We report a neutron diffraction and muon spin relaxation $\mu$SR study of static and dynamical magnetic properties of ${\mathrm{BaCo}}_2{\mathrm{V}}_2{\mathrm{O}}_8$, a quasi-one-dimensional spin-chain system. A proposed model for the antiferromagnetic structure includes: a propagation vector ${\mathrm{k⃗}}_{\text{AF}}=(0,0,1)$, independent of external magnetic fields for fields below a critical value $H_c(T)$. The ordered moments of 2.18 ${\mu }_B$ per Co ion are aligned along the crystallographic $c$ axis. Within the screw chains, along the $c$ axis, the moments are arranged antiferromagnetically. In the basal planes the spins are arranged ferromagnetically (forming zigzag paths) along one of the axes and antiferromagnetically along the other. The temperature dependence of the sublattice magnetization is consistent with the expectations of the three-dimensional (3D) Ising model. A similar behavior is observed for the internal static fields at different muon stopping sites. Muon time spectra measured at weak longitudinal fields and temperatures much higher than $T_N$ can be well described using a single muon site with an exponential muon spin relaxation that gradually changes into an stretched exponential on approaching $T_N$. The temperature-induced changes of the relaxation suggest that the Co fluctuations dramatically slow down and the system becomes less homogeneous as it approaches the antiferromagnetic state.