The Icelandic star donned a pink fair-style dress to the celebrity showing at the Palais des Festivals on Wednesday evening.
She paused on her way up the red carpet to pose for photographers, curtsying, but blinking and turning away if anyone moved too close.
The 31-year-old singer arrived arm-in-arm with her co-star, French actress Catherine Deneuve, who earlier in the day had told reporters how Björk often found work on the film overwhelming.
She said: "Sometimes she couldn't take what she was doing. It was like a little child running away from school.
"Sometimes she would run away."
But Deneuve was greeted with applause at the press conference when she said she understood Björk's behaviour, and it should not be allowed to eclipse her performance in the film, which is one of the 23 in the running for Cannes' top prize, the Palme d'Or.
In the film, directed by Lars Von Trier, Björk plays a poor Czech immigrant in the US who fantasises about appearing in a Hollywood musical.
Deneuve, 56, said: "No film is without tension, without difficulties. Björk is a wonderful person, but she's very special.
"She cannot really act, she can feel in the film."
She added: "Let's not let the fact that Björk cannot be here today, that she cannot speak about what she's done, be the centre, because that's not what the film's about."
Lars Von Trier - best known for films such as Breaking The Waves and The Idiots - said the singer, who shot to fame in the mid-1990s with her first solo album Debut, was his first choice for the lead role.
He added he was sure she would one day "come out" to talk about her part - as Deneuve joked "in 10 years".
"Björk is not an actor, which is a surprise for me, because she seemed very professional," he said.
"She's not acting anything in this film, she's feeling everything, which is incredibly hard on her and hard on everyone else.
"It's like being with a dying person. She was really feeling this all the time, the core of this person.
"This work with Björk has been very rewarding for both of us, but also very painful."
Dancer In The Dark is not the 34-year-old singer's movie debut; she appeared in lcelandic film Juniper Tree in 1987 when she fronted cult pop band The Sugarcubes. She also took a cameo part in 1994's Pret A Porter.
Her distrust of the press is well-known. In February 1996, she attacked reporter Julie Kaufman in front of TV cameras at an airport in Bangkok.
She later apologised, saying she was trying to protect her son from media attention.
A spokesman said: "Geri is here to meet people and do some interviews for trade papers, but there will be no press conference or photo call."