In most cases OpenVZ hosting will use OpenVZ 6 with an outdated kernel which is incompatible with Docker.
Docker is only supported with OpenVZ 7 (based on 3.x kernel, see https://openvz.org/Docker_inside_CT_vz7 ) or with OpenVZ 6 with kernel version 042stab105.4 or newer (see https://openvz.org/Docker_inside_CT ).