It was unclear why Javier Montojo Salazar fell from the ship on Friday evening, not far from the Spanish "Juan Carlos I" base on Livingston Island.
Rescuers searched for his body for six hours before finding it, the ministry said in a statement.
The Hesperides ship is now travelling to Ushuaia in Argentina to start the process of repatriating the body.
Defence Minister Maria Dolores de Cospedal tweeted her condolences to Montojo's relatives and loved ones. "Rest in peace," she said.
Hesperides is a ship that conducts research into marine biodiversity and other issues, and is also used to provide supplies to Spanish bases in Antarctica given its hull is reinforced, allowing it to navigate in icy waters.