The recording of Verdi's Ernani in 1903 by the Italian Gramophone Company, a part of HMV was the first complete opera recording. It was issued on 40 single-sided discs. The first complete orchestral recording, Arthur Nikisch's recording of Beethoven's Fifth Symphony, was made in 1913.
References
Ernani (1903 HMV recording) Wikipedia(Text) CC BY-SA