Shortly after departure, the flight attendant began beverage service. She slipped on the main cabin door floor area and injured her left arm. The flight attendant was unable to perform her crew duties; however, an airline pilot, who was a passenger on the flight, assisted in maintaining cabin safety. The flight attendant reported that there was de-icing fluid on the floor of the floor which made the surface slippery. Deice fluid was present on the ramp areas surrounding the airplane.