B767-200
Flight Crew Air Transport Pilot (ATP); Flight Crew Flight Instructor
Flight Crew Last 90 Days 143; Flight Crew Total 17000; Flight Crew Type 2370
Flight Deck / Cabin / Aircraft Event Illness / Injury; Inflight Event / Encounter Weather / Turbulence
General Physical Injury / Incapacitation
Weather
We had departed a non-controlled airport. We had received our clearance via cell phone from ZZZ and had departed under VMC conditions prior to our clearance void time. The initial cruise altitude was FL240 and were to contact ZZZ on HF for further climb due to additional inbound aircraft. My copilot was the flying pilot and we were at initial assigned cruise altitude FL240. We were contacting ZZZ radio on HF for further climb clearance to FL380 when we encountered moderate turbulence for approximately 10 seconds. The flight conditions were smooth and showed nothing on the radar prior to and after this event. The Flight Attendants (FA) were preparing for the initial food and beverage service. Post turbulence I was informed by the 'A' FA of injuries to a flight attendant involving her ankle and 2 cuts on her face from a beverage cart. As soon as time permitted I requested the door to be blocked so I could go back and check on her myself. She seemed comfortable and had her leg up and ankle on ice.I was not aware until landing that 2 other FAs were additionally injured; one who complains of hurt back and one who complained of a knee injury.
B767 Captain reported encountering unforecasted and undetected moderate turbulence at FL240 that resulted in injuries to three flight attendants.