The Danish Veterinary and Food Administration claims that if eaten regularly, the products could damage children's livers and kidneys.
Kellogg's says its cereals are within recommended daily vitamin allowances.
In the UK, the Food Standards Agency has advised people to carry on eating cereals as part of a healthy diet.
Kellogg's had asked the DVFA if it could add iron, calcium, vitamin B6 and folic acid to 12 cereals and six cereal bars.
A spokeswoman for the DVFA said that an evaluation of the amount of vitamins and minerals consumed by people in Denmark meant that the proposed new levels would "have a high impact".
"The amounts proposed could be harmful to general health or food safety", she added, reports BBC. co.uk
Chris Wermann, director of corporate affairs for Kellogg's in Europe, said: "Most of us are a bit incredulous." The extra B6 and folic acid accounted for a quarter of a person's daily allowance, and the calcium and iron just 17%, he said. "It is quite clear from nutritionists that diets around the globe are deficient in vitamins and minerals. We are quite worried about the Danish authorities challenging this. We don't believe there is any danger at all. There is every reason for people to have these."
He added that details of added ingredients were labelled clearly on products and were well within recognised international guidelines.
Mr Wermann said: "The Danish diet is pretty frugal or austere at the best of times. They are protective of their diet. Equally the government is working in their country to take extra vitamins and minerals in their diets. We are not too sure where they are coming from on this one."
The company is planning to have further discussions with the Danish authorities, informs Guardian.co.uk