United Airlines flight 128 encountered moderate turbulence while at FL360 and about 60 miles southeast of Jamaica, and a flight attendant (FA) sustained a serious injury. The flight crew reported that while at FL360, in visual meteorological dark night conditions with no indication of an adverse ride from their onboard weather applications or their weather radar, the flight encountered about 3-5 seconds of moderate turbulence. The fasten seatbelt sign had been illuminated about 15 minutes earlier due to an area of light turbulence and remained illuminated during the event. The captain stated that upon encountering the moderate turbulence he immediately made a public address announcement “flight attendants be seated immediately, be seated immediately”. Following the turbulence encounter the flight crew asked the flight attendants to check in and were advised that a FA had been injured. The FA assigned to jumpseat 2R reported that they had been seated with their seatbelt fastened for about 10-15 minutes due to a previous announcement from the fight deck about an area of light turbulence. With no turbulence encountered for several minutes the FA elected to stand and began preparations for the water service. When suddenly and without warning, the airplane “violently shook” throwing them into the right galley wall. Their lower back impacted a quarter turn utilized to secure the service carts. Upon being notified of the injury, the flight crew contacted MedLink and the decision was made to continue to George Bush International Airport (IAH), Houston, Texas. Paramedics met the airplane at the gate and transported the injured FA to the hospital where they were diagnosed with a serious injury. At the time of the turbulence encounter there were no active significant meteorological information (SIGMETs), convective SIGMETs, airman’s meteorological information (AIRMETs), or pilot reports (PIREPs) of any significant turbulence.