The audience booed the Netflix logo, which appeared before the film started, and it then became clear the film was playing in the wrong aspect ratio.
After the jeers, the movie was stopped and restarted without explanation.
Some film journalists in the screening uploaded videos of the heckling on social media.
The BBC's Lauren Turner, who was at the screening, said: "There was shouting from the upper seats and it became apparent the aspect ratio was wrong, so they restarted it after about 10 minutes.
"The second time around the audience booed the Netflix logo again. But there was also some cheering at the same time and a warm round of applause at the end."
A statement from the Cannes Film Festival said: "This incident was entirely the responsibility of the Festival's technical service, which offers its apologies to the director and his team, to the producers and the audience."
On Thursday, there was also some booing when the Amazon logo came up at the beginning of Wonderstruck, which stars Julianne Moore and Michelle Williams.
Earlier this week, Cannes jury chair Pedro Almodovar said he agreed that films should have to be screened in cinemas if producers want them to be considered.
Indiewire film critic David Ehrlich tweeted: "Okja starts, huge boos at Netflix logo. Then film plays in wrong aspect ratio and Grand Lumiere almost rioted. Movie stopped."
The Telegraph's Robbie Collin wrote: "Cannes making an A+ case for the primacy of the cinema experience by projecting the first ten mins of Okja in the wrong aspect ratio."
Blogger Elena Lazic said: "That didn't start well. Screen not open properly, significantly cropped at top... the boos at the Netflix logo were immediately followed by boos at the terrible projection."
The film is a South Korean-American adventure movie about a young girl named Mija who tries to prevent a multi-national company from kidnapping her best friend, a massive super-pig named Okja.
Speaking after the film, director Bong Joon Ho said he "loved working with Netflix", adding it was a luxury to be given such a huge budget for it.
Swinton said: "It's an enormous and really interesting conversation that's beginning. But I think, as in many matters, there's room for everybody."
Gyllenhaal added: "It's important to have artistic expression in whatever form we can.
"Debate is essential always. It's a useful thing to have this discussion about how art is perceived and distributed."
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