The organisation said it had written to Sony Pictures executives in Japan to ask the studio to emphasise that the film was a work of fantasy.
Based on Dan Brown's novel, The Da Vinci Code claims Jesus Christ married Mary Magdalene and had children, which was covered up by the Catholic Church.
Sony has said it is not a religious film, and is not meant to criticise.
"Some media have written that Sony is examining the possibility of putting at the beginning of the film an announcement to clarify that it is a work of fantasy and that any similarity with reality is purely coincidental," Opus Dei said in a statement.
"Any such decision by Sony would be a gesture of respect toward the figure of Jesus, to the history of the Church, and to the religious beliefs of viewers."
Opus Dei, which critics say is secretive and ultra-conservative, has previously called for changes to be made to the film's final edit, and asked for it to be given adults-only ratings.
Other members of the Roman Catholic Church have also voiced their concern.
On Good Friday, the preacher for the papal household denounced theories which he said made huge profits in denying the teachings of the Catholic Church.
"Christ is still sold, but not any more for 30 coins, but to publishers and booksellers for billions of coins," Rev Raniero Cantalamessa said in a homily at St Peter's Basilica.
"No-one succeeds in stopping this speculative wave, that instead will register a boom with the imminent release of a certain film."
However, he did not refer to the film or Dan Brown's novel by name.
The movie, which stars Tom Hanks and Audrey Tautou, will open this year's Cannes film festival on 17 May, two days before it is released worldwide.