An EU/EEA citizen is covered by the right to free movement in Europe and does not need a work permit to work in Sweden.
Anyone who is a family member of an EU/EEA citizen with a right of residence in Sweden, but who are themselves a citizen of a non-EU/EEA country, may also work without a work permit. However, they must apply for a residence card if they will be here for more than three months.
You want to employ – Person with a residence card
Countries covered by the right to free movement within Europe
Below you can see which countries are covered by the right of free movement, both on the map and in a complete list.