Air carrier pilot reported encountering severe turbulence resulting in an injury to a Flight Attendant by a dislodged fire extinguisher.

Narrative

Operating the flight from ZZZ1-ZZZ we were in cruise at FL310 over Location A and the flight was smooth up to this point. We were direct to the ZZZ VOR and ATC gave us a descent to FL290. As we got closer to the ZZZ area we began to enter in and out of IMC and encountered severe turbulence. The flight attendants were notified ahead of time that the flight was going to begin to get bumpy and we had the seatbelt sign on. While we were in the turbulent area there was nothing showing on our radar for storms cells and ATC did not have any reports from aircraft ahead of us for severe turbulence. LCA (Line Check Airman) asked for left deviations because that area appeared to be clearer as well as a descent to try and get below the weather. We were given vectors to the left as well as a descent down to FL240. Upon reaching FL240 things began to smooth out but during the flight through the area of turbulence we experienced altitude gains and losses of 300ft as well as rolls of up to 25 degrees. Airspeed and pitch also experienced deviations but I am unsure of how much we deviated. Once we were in smoother air LCA handed me control of the aircraft so he could talk to the flight attendants. He informed me that none of the passengers were injured but multiple did vomit and that FA (Flight Attendant) Person A was injured. I gave LCA control of the aircraft back after he was done informing me. As we approached ZZZ I called the flight attendants to get the arrival information from them. That is when FA Person B informed me of FA Person A's injuries. FA Person A was seated in the aft of the cabin and during the turbulence the overhead bin where the fire extinguisher is store opened; the fire extinguisher came out of its secure latch; fell out of the bin and hit FA Person A in head injuring their eye. FA Person B was also in the aft cabin during this time and informed me that during the turbulence the headrest for the jumpseat fell off and hit them. Once we arrived in ZZZ I conducted the post flight walk around while LCA coordinated with Dispatch; ops; and Maintenance. I did not notice any visible aircraft damage during the post flight. We had medical assistance come out to help FA Person A and they left with them. FA Person B was uninjured but was shaken and called out for the rest of the day. LCA wrote up the jumpseat headrest; the fire extinguisher; and the severe turbulence in the maintenance log.A widespread weather event throughout the northeast carried pockets of severe turbulence. This cause the fire extinguisher to fall out resulting in FA Person A's injury; as well as the jump-seat headrest to fall off.