Danish universities are concerned by an influx of Swedish medical students with higher grades than home applicants.
They are worried that Swedes find it too easy to gain admittance to university in Denmark. This year, Swedish applicants have been allocated almost a quarter of all places.
Helge Sander, the Danish Minister of Science, Technology and Innovation, blamed the differences between the countries' education systems, especially examinations and grading.
"We've got to look more closely at how we evaluate applications from Sweden," Ms Sander told the newspaper Politiken. "It's important we have a fair system, one that doesn't judge our own students too harshly."
She believes the selection procedure, based on a grade-point average, favours Swedes because they take fewer examinations than the Danes. Swedes are also entitled to retake as many school exams as they wish if they want to improve their grade-point average. In Denmark, only failed exams can be retaken.
The Danish Government has decided that Swedish students will now need a higher grade-point average than Danish students to be admitted to university.
Jakob Lange, a Danish consultant in education policy, said the measure did not go against the European Union's stipulation that applications from different member states be judged equally.
He said: "We're working closely with the Swedish Ministry for Education, getting a clearer picture of just what Swedish qualifications entail. This allows us to make sure we judge Danes and Swedes fairly."
Lars Lustig, of Sweden's Umea University, who recently conducted an assessment of university admission procedures for the Swedish Government, said national entrance exams in subjects such as medicine and dentistry would be the fairest way to assess the suitability of all applicants, no matter what their country of origin.