B737-800 First Officer reported a Flight Attendant was injured during a wake turbulence encounter on descent into SEA in trail of an A380.

Narrative

Seattle Center cleared our flight to descend pilot discretion from FL340 to FL240. Within moments the Captain initiated the descent using altitude intervene. We were within 50 miles of top of descent and the cruise descent rate initiated at 1000 feet per minute. Within a minute Seattle Center gave us a frequency change and we checked in with a new Controller. Approximately 60 seconds after checking in with the new Controller we observed an Airbus 380 at our 10 o'clock. It had flown across our path from right to left (we were traveling NW bound on the Chins arrival) at what I would guess was FL360. We were descending through an altitude of approximately FL300 when we observed the Airbus 380. About 60 seconds later we encountered residual wake turbulence from the Airbus 380. About 20 seconds later the A Flight Attendant called over the interphone to indicate she may be injured. She requested medical attention upon arrival and after deplaning. Immediately following the Flight Attendant call I informed Seattle Center of the wake turbulence and possible injuries on the aircraft. About 60 seconds later we were contacted by Seattle Center inquiring about the details of our encounter and severity of injuries. I then initiated contact with Dispatch to relay the request for medical attention. I then followed up with Operations when we were on the ground and clear of the runways that medical staff would be present at our gate. Upon arrival at the gate; medical staff was present. Passengers deplaned; and all of the flight attendants requested to be examined by medical staff.Seattle Center never made us aware of the Airbus 380 traffic and because we were in a descent and well below the altitude of the [Airbus] 380; we were not alerted. I will be more vigilant looking for traffic during descents when my vision is blocked by the airframe with pitch attitudes different than cruise. And I recommend extra vigilance by ATC when the Airbus 380 is in the vicinity of other aircraft. They are rare to see and their wake turbulence profile is much larger than even I expected. This event was my first encounter with the Airbus 380.