B737 Captain reported during taxi an aircraft at a gate was pushed back toward them requiring abrupt braking to avoid a collision. As a result; a flight attendant fell and hit their head and the flight returned to the gate.

Narrative

They pushed us out of [Gate] XX east onto the ramp and approved us to do our crossbleed start right there. Once this was done we got clearance from the Ramp Controller to taxi out to spot XY and contact Ground. Following the taxi line we started to make our way to spot XY. We were coming up on XZ when all of a sudden I see the airplane that was parked there (A321) being pushed toward us. To avoid a collision I had to apply the brakes abruptly. I came to a full stop; set the parking brake and called ramp to clarify what was going on and they told me that they did clear the plane at XZ to push and that it should not have been a problem. Before continuing to taxi I called the Flight Attendants to make sure they were ok. This is when I was told by the #1 Flight Attendant (FA) that he fell and hit his head but felt good enough to continue to ZZZ1. We made it out to spot XY and were told by Ground Control that it would be several minutes before they could allow us to taxi to our runway. The parking brake was set and I wanted to make sure the #1 FA was ok. I called the back and he told me he wanted me to see his head and if it was ok to do so. I saw a big lump on his head so I gave him the option to either return to the gate in ZZZ or to seek medical attention in ZZZ1 when we arrived if he felt the need to do so. He decided the best course of action would be to return to the gate for medical assistance in ZZZ. I asked him if he wanted us to call the medics but he refused and told me he would go to the company clinic in the terminal. Cause: There would have been a chance that I could have heard the push clearance for XZ. However per SOP; Captains are not allowed to monitor the ramp frequency.