United Airlines flight 2197 experienced clear air moderate turbulence at flight level (FL) 350 while enroute to Toronto Pearson International Airport (YYZ), Toronto, Canada. The flight was a regularly scheduled passenger flight from George Bush Intercontinental Airport (IAH), Houston, Texas. As a result of the turbulence, one flight attendant experienced a serious injury to their wrist. The aircraft received no damage and continued to its destination without further incident. As stated by the first officer, dispatch remarks for this flight included a forecast for light to moderate turbulence over VORTACs BUM - JOT between FL310 - 390. The captain conducted a pre-departure briefing with the flight attendants which included the possibility of experiencing turbulence. About two hours into the flight, two flight attendants were in the last three rows of the aft cabin conducting in-flight service when light turbulence commenced. The two flight attendants decided to “bring the cart back into the galley to finish the service.” As they were pushing back into the galley, the turbulence intensified, and one of the two flight attendants asked the other to sit down in their jump seat while the other set the brake on the cart. As the flight attendant was securing the cart, the captain made an announcement asking the flight attendants to take their seats. At that time, the flight attendant who was securing the cart lost their footing and fell back where the other flight attendant had taken their seat. The seated flight attendant attempted to brace the falling flight attendant and injured their wrist. The captain stated that this instance of turbulence lasted about 15 seconds. In addition, he reported that that the seatbelt sign had been on for five minutes prior to this moderate turbulence as the aircraft flew through light turbulence earlier in the flight. The injured flight attendant was treated by an onboard doctor, and the flight proceeded to its destination without further incident. Upon arrival to Toronto, paramedics met the airplane. The flight attendant was taken for x-rays and diagnosed with a broken bone in their wrist.