The boycott, which Arla says is now almost total, began after news media in several Middle East countries showed cartoons of the Prophet Muhammad that were published in Danish newspaper Jyllands-Posten in September last year.
One of the 12 cartoons depicted Muhammad wearing a bomb-shaped turban.
Arla, which counts the Middle East as one of its biggest growth markets, has taken a large slice of the backlash. It said its warehouses were full after all customers in the region cancelled their orders for its dairy products.
The group is currently deciding whether or not to suspend production for the Middle East.
"Once sales in the Middle East have come to a standstill, this inevitably has consequences for the production," says Jens Refslund, director of Arla's Production Division. "A decision about what we do next will be taken within the next few days. After that, staff will be informed."
The financial fallout could be serious, with Arla collecting around €348.4m per year in sales from the region. It also recently announced a plan to increase this to €549.9m over the next five years, requiring the group to double its Middle East workforce.
Louis Honoré, Arla spokesperson, had said the firm was planning a multi-million Danish Kroner investment in the Middle East region, including factory extensions and a pilot plant to test new products and packaging.
Several supermarkets across United Arab Emirates, Bahrain, Quatar, Kuwait and Saudi Arabia said on Sunday they were removing all Arla products from their shelves. The Danish firm, meanwhile, reported that two of its staff had been beaten up in Saudi Arabia.
E-mails and text messages detailing the names of Arla products have also begun circulating in Saudi Arabia.
Denmark's ambassador to Saudi Arabia, Hans Klingenberg, attempted to quell the unrest by reiterating Denmark's respect for all people and religions. Jyllands-Posten, the newspaper involved, has also now issued a public apology for the cartoons.
Arla paid for adverts quoting amabassador Klingenberg after the local press did not publish his comments, yet Arla's executive director, Finn Hansen, said it would take more than that to calm the situation.
"This is what we can do. Based on our many years of experience in the Saudi market, however, we're not particularly hopeful that it will achieve the desired effect. The only thing that can stop the current boycott of Danish products is a direct dialogue between the parties involved."
An Arla spokesperson told DairyReporter.com last autumn that the group's Puck cheese brand was almost as well-known as Coca-Cola in the Middle East. Its Lurpak brand also leads the region's butter market.
He added that Arla had been producing dairy products in Saudi Arabia for so long that "we believe the authorities consider us a local dairy". The firm also announced last year it would move production of processed cheese at its Bislev Dairy in Denmark to Saudi Arabia.