Arnold also added wryly that maybe 2011 "was a good year".
The letter sarcastically applauded the selectors saying they had "returned to their senses" and added: "Men love their women to have depth, but only when it comes to their cleavage."
The only woman to win the award in the festival's 64-year history is New Zealander Jane Campion for The Piano in 1993.
The head of the selection committee, Thierry Fremaux, said the judges would not select a film that doesn't deserve it "just because it is directed by a woman".
The jury, which also includes actor Ewan McGregor, director of The Descendants Alexander Payne, and designer Jean Paul Gaultier, initially met on Wednesday. The president of the jury, Nanni Moretti, said they would meet every two days to discuss the competing films.
Wes Anderson opened the festival with his meticulously composed ode to young love Moonrise Kingdom.
The premiere announced the start of 12 days of the most selective festival slate in cinema, with eagerly anticipated films to follow from many of the world's most esteemed directors. That is, when a camel isn't running amok.
Sideshows are as much a part of Cannes as the main events, a tradition kicked off this year by Sacha Baron Cohen.
The comedian again promoted his upcoming film, The Dictator, with a stunt, this time taking a humped mammal on a stroll down the Croisette, Cannes' famous promenade.
The more dignified, black-tie-only opening ceremony was hosted by Bernice Bejo, who starred in The Artist which won a best picture Academy Award. In attendance, along with the cast of Moonrise Kingdom were Jane Fonda, Eva Longoria, Lana Del Rey and Alec Baldwin, who gallantly carried his fiancee, Hilaria Thomas, up the many stairs of the Palais.
The jury of will sift through the 22 in-competition entries to decide the festival's top award, the prestigious Palme d'Or.
- Independent, AP