Permission to work in Denmark
Citizens from the Nordic countries
If you are a citizen of one of the Nordic countries, you have the right to work in EU countries including Denmark. Therefore, you do not need a work permit or a residence permit to work in Denmark.
Citizens of other EU/EEA countries
If you as a citizen of any other EU/EEA country move to Denmark and stay there for more than three months, you may need to apply for a "opholdsdokument" at the "Statsforvaltningen" or the International Citizen Service in Copenhagen. You should then be able to show proof of employment or a confirmation of engagement from the employer.
EU/EEA citizens can in principle accept a job in most professions. There are, however, certain professions, which can require that you are a citizen of the country. This can include some services within the police, judiciary work, the armed forces and public administration.
Citizens from countries outside of the EU/EEA
If you live in Sweden but are a citizen from a country outside of the EU/EEA, you do not have the automatic right to work in or move to Denmark.
Generally, if you have lived in an EU country, such as Sweden, for five years, you can get a status of "long-term resident", which means that you are able to move on to another EU country to work. But it is important to be aware that these rules on "long-term residents" do NOT apply to Denmark and Ireland.
Visit Nyidanmark.dk to get more information on your possibilities to apply for a residence- and work permit in Denmark. Beware that in some cases your residence permit in Sweden can be affected if you work in another country.
For more information please contact Migrationsverket (The Swedish Migration Agency).