B737-700 Captain reported the aircraft separated from the tow bar during pushback. The pilot indicated being notified by the ramp crew to apply brakes immediately; and the aircraft returned back into the gate for a maintenance inspection; and no damage noted.

Narrative

During pushback from ZZZ Gate XX; the aircraft separated from the tug towbar. The Ramp Crew urgently requested that the Captain apply brakes; which I expeditiously did. With the aircraft stopped; I elected to have the aircraft towed back into the gate and inspected by Maintenance because I was not sure if the pin sheared or if the towbar was somehow not secured to the nose landing gear.At the gate; Maintenance determined that the pin didn't shear and that there was no aircraft damage. Further; they had reviewed the incident and determined the aircraft did separate from the towbar (as the Ramp Crew had advised). My supposition; after talking to the Ramp during the event and Maintenance after the event; is that somehow the Ramp Crew had improperly attached the towbar and pin to the nose gear. This created a faulty connection that subsequently released during the pushback.The FA's (Flight Attendants) confirmed that they were okay and did not desire medical attention from the abrupt stop. One Passenger expressed a concern that her hip may have been hurt by the event (seated with seatbelt fastened). We brought ZZZ EMT's onboard to provide medical attention. The Passenger adamantly refused medical attention and desired to travel. The ZZZ Station; the Dispatcher; and I agreed that she would be okay to travel. Subsequently; we pushed again; and the flight continued uneventfully to ZZZ1.Ramp connected the towbar just prior to push so Pilot inspection would not have caught this error. In addition; Ramp gave the appropriate responses during pushback flight interphone communications. Therefore; it is my assumption that they believed the towbar was attached properly. My inclination is that a more thorough review of towbar hookup procedures would help new Ramp Agents to ensure the connection was secure. I applied the brakes abruptly. The urgency of the Ramp brake request made me feel that danger or a conflict was directly imminent. I did not have time in my reaction to consider the FA's position. They could have been seriously hurt. Fortunately; they were Safety demo complete" and mostly just destabilized briefly. This could present an opportunity in a future recurrent training to practice a smooth brake application in reaction to an urgent external request."