Finn Hansen, Arla's executive director, said it would take a long time for the Danish dairy firm to re-establish the business and good trading relations it had in the Middle East until one week ago.
Peder Tuborgh, the group's managing director, agreed: "This could take years, but we want to see a dialogue that can solve the conflict and allow us to work towards re-establishing Arla's business in the Middle East."
Their words of caution came as Arla announced it had ceased all production for its key Middle East dairy market, which brings the firm around €348.4m in sales per year.
The long-term financial fallout could be just as serious, with the Middle East viewed as a key growth region by Arla. It recently announced a plan to increase sales there to €549.9m over the next five years.
The group said its 1,200 employees in the Middle East would be kept on "to ensure that Arla can quickly restart production if consumers are prepared to buy Danish products once more".
The decision to halt production was made after Arla, which has been in the area for 30 years, found itself at the centre of a near total boycott of Danish products across several Middle East countries.
Many Muslims were incensed following local media reports showing cartoons of the Prophet Muhammad, published by Danish newspaper Jyllands-Posten in September last year. One of the 12 cartoons depicted Muhammad wearing a bomb-shaped turban.
Most supermarkets across United Arab Emirates, Bahrain, Quatar, Kuwait and Saudi Arabia have now removed Arla products from their shelves.
The boycott has persisted despite an apology for the cartoons from the Jyllands-Posten newspaper, and public appeals by Denmark's ambassador to Saudi Arabia, Hans Klingenberg; who reiterated Denmark's respect for all people and religions.
Arla's Tuborgh said there was at least now a platform for discussion. He said it was not Arla's responsibility to solve the conflict, "but we would like to contribute to a dialogue between the parties and urge them to find a solution".