“If the vaccine is effective and safe, Denmark will receive enough doses so that around 2.4 million Danes can be vaccinated,” Health Minister Magnus Heunicke told reporters.
“But the aim is that all Danes will be offered a vaccine,” he said.
Denmark is home to some 5.8 million people.
Pharmaceutical companies around the world are racing to develop vaccines against the new coronavirus.
The EU has so far reached agreements with Sanofi-GSK, Johnson and Johnson and CureVac, in addition to AstraZeneca.
AstraZeneca said in July that its vaccine, developed together with the University of Oxford, should be available by the end of the year.
Denmark on Friday reported a total of 16,525 cases and 621 deaths linked to the new coronavirus.