HMHS Britannic was sunk by a mine, very likely laid only about an hour earlier by the German submarine U-73. No submarines are known to have been in the area and fired torpedoes, and it is known that U-73 was laying mines in the area.
U-73 had a successful minelaying career in the Mediterranean, probably sinking 13 ships by mines, and damaging a further 2 (of a total of 21 sinkings, and 3 damaged). It's difficult to be certain about sinkings by mines, especially since no detailed record of exactly where she laid mines survived. These sinkings were in areas where U-73 is known to have laid mines, and she is the most likely culprit.
HMHS Britannic was almost half of the total tonnage sunk by U-73, which also included two pre-dreadnoughts (the British HMS Russell and the Russian Peresvyet). Most of her victims were small.
For a list of U-73's known and suspected sinkings, see: