The production, directed by Deborah Warner, lent a feminist slant to the opera and was staged in modern dress on a platform suspended by wires.
At one point Don Giovanni, sung by Gilles Cachemaille, petted and kissed a statue of the Virgin Mary and then rubbed himself against it. Booing at Glyndebourne has been a rare occurrence in its long history. The last case was in a production a few years ago of The Magic Flute, set on a Los Angeles beach, which dispensed with all the recitative. But the audience at the first night of Don Giovanni, on Sunday in the new pounds 31m opera house, were even more vociferous.
The singers were applauded but there was loud booing when Deborah Warner and her design team of Hildegard Bechtler and Sue Blane came to take their curtain call.
Anthony Whitworth Jones, general director at Glyndebourne, commented: 'It's sad but we've just got to get over it. In fact the scene at the end was a very jubilant one. There was gigantic applause, every singer got huge adulation, Deborah got huge applause and there were some boos.
'One person near me was urgent and vigilant in his booing. Then there was cheering again and a contest in which the cheers won. There was one thing that bothered some people, the treatment of a Madonna statue which the don picks up in the graveyard and sort of abuses, caresses and behaves absurdly. If that is the nub of it then it's very depressing. Of course its outrageous, sacrilegious behaviour, but it's right in the context.'
Ms Warner's last production in Britain was Samuel Beckett's play Footfalls, which at 20 minutes was the shortest play ever presented in the West End.