B737 flight crew reported loss of control during gate pushback when the tow bar disconnected from the aircraft. A flight attendant was injured in the abrupt stop.

Narrative

During pushback in ZZZ; the tow bar disconnected from the tug. The push crew said 'STOP STOP' into the headset; and gave the emergency brake hand signal as the headset had disconnected from the jacks on the airplane. I hit the brakes and the airplane jerked to a stop. While I set the brake and reestablished communication with the ground crew; I had the FO call the flight attendants and confirm the status of the cabin. It was reported that everyone was ok; and there was zero aircraft damage; so we elected to continue the flight.Reaching cruise flight; we received a call from the purser that the forward flight attendant had hit her back on the corner of the galley and even though she initially felt fine; was now in a lot of pain and unable to turn her back. The purser seated the FA in an open seat; gave her ice; and found a nonrev flight attendant seated in 20B; who was willing to sit in the jump seat and assist in flight duties. I contacted dispatch via ACARS to let them know of the situation; who contacted the inflight duty manager and the Chief Pilot to notify them of the situation. I did not contact the medical advisory service due to the short duration of the flight as we only had 40 minutes remaining. We did not ask for EMTs at the gate; the FA wanted to go the clinic during their long sit in ZZZ1.Upon arriving at the gate; the ZZZ1 inflight supervisor met us at the aircraft to take the FA to the clinic; I walked to where the FA was seated to check on her and exchange information. She appeared to be in a lot of pain; on the verge of tears.