The game is inspired by real-life "ghost ships" like the Mary Celeste, which was found in 1872 adrift and deserted in the Atlantic Ocean; the fate of its crew and passengers is still debated by historians.
The Obra Dinn itself is modeled on the HMS Leopard, a Royal Navy vessel employed during the Napoleonic Wars; although the ship's appearance is fairly accurate and realistic, it is smaller than its real-life counterpart and, even with its reduced scale, would have been considerably undermanned with the crew portrayed in the game.
There was, however, no real ship named Obra Dinn and the events of the game are fictional.