The decision comes after the tabloid made the decision to publish the controversial Kate Middleton topless photos, becoming the third publication to do so after French magazine Closer and Italian magazine Chi.
The International Business Times reports that the paper is funded by a joint venture between Independent News and Media, based in Ireland, and the UK-based Northern & Shell, which is chaired by Desmond.
The 60-year-old told Sky News: "I am very angry at the decision to publish these photographs and am taking immediate steps to close down the joint venture.
"The decision to publish these pictures has no justification whatever, and Northern & Shell condemns it in the strongest possible terms."
Desmond's comments were echoed by Gareth Morgan, the editor of Daily Star Sunday in the UK, who said: "We're absolutely horrified here in the office, and as a company. This has no merit as an editorial decision, it has no merit morally, it's frankly a horrible decision."
St James's Palace has announced their plans to sue Closer magazine for the initial publication of the photos, and have also released a statement comparing the invasion of privacy to "the worst excesses of the press and paparazzi during the life of Diana, Princess of Wales".