Flight Crew Commercial; Flight Crew Multiengine; Flight Crew Instrument
Flight Crew Type 1600
Communication Breakdown; Distraction; Other / Unknown
Flight Deck / Cabin / Aircraft Event Illness / Injury; Inflight Event / Encounter Weather / Turbulence
Flight Crew Regained Aircraft Control; General Physical Injury / Incapacitation
Weather
I was the Pilot monitoring on flight to ZZZ when we encountered moderate turbulence enroute at FL340 in Monterey airspace over the gulf of Mexico over the fix of XOTUG. It went from completely smooth air to moderate turbulence with a couple of jolts and rolls to where it caused several injuries to passengers and flight attendants where we had paramedics meet the aircraft upon arrival in ZZZ. We did not have any indications on RADAR nor from ATC that it was moderate level turbulence and we were completely startled ourselves. It only lasted about 10-15 seconds while the autopilot remained on and smoothed out afterwards. We checked on the cabin status and were told of the injuries incurred by the passengers who one happened to be in the lavatory and one who had coffee spilled on her lap. The Flight Attendant also hurt her wrist and hip as well from what we were told. Prior to this; the seat belt sign was off as we were experiencing smooth air and we turned it on as soon as we encountered the turbulence. We also made the PA announcement for the flight attendants to remain seated.
B737 First Officer reported moderate turbulence with minor injuries to passengers and flight attendants.