Air carrier flight crew reported the tow bar disconnected during pushback procedure from gate.

Narrative

We were ready for pushback; pre-push items complete and this would be a four-person wireless pushback. I released the brake and told Tug Driver; 'Brakes released cleared to push tail south at a 45.' At Gate XX; there is a hard turn to the Tug Drivers left; to push clear of vehicular roadway. As he was getting ready to make that turn; the towbar disconnected completely from the aircraft; but the crew was unaware of that until the Tug Driver gave me the instructions of; 'Captain; set parking brake.' This caught me off guard because the aircraft was still moving backwards and we thought the tug was still pushing us back. I questioned the Tug Driver and he again stated to set the parking brake. That's when we realized we had become disconnected from the tug. We were still moving backwards; so I carefully applied the brakes; and the aircraft came to a stop and I set the parking brake. I asked him what happened and the Tug Driver said when we rolled over the fuel station on the ground; the towbar rolled over on its side and disconnected from the aircraft. Maintenance was called out to the aircraft and they inspected the aircraft and gave us the go ahead to proceed. I called the Chief Pilot. He also advised we were good to go. They reconnected the tow bar; we continued the push; and flight was completed. Ground Crew needs to be sure the towbar is properly connected. We suspect it was not.