The EU pet passport is the standard document for moving a pet between EU countries, including into Sweden, and it's issued only to pet owners resident in the EU by an authorised vet in their home country. It records the microchip number and the rabies vaccination history, and it stays valid for the pet's life as long as the vaccination record is kept up to date.
Travellers resident outside the EU need an animal health certificate instead, under the same EU Regulation 577/2013 framework that applies across the bloc, confirming the microchip and vaccination requirements. If you're arriving from a country not on the EU's low-rabies-risk list, a rabies antibody blood test is also required, taken at an approved laboratory at least three months before the pet can enter.
Norden.org's guidance is clear that the exact requirements can vary by the country you're travelling from and the pet's age, and it points travellers to Jordbruksverket, the Swedish Board of Agriculture, for the country-specific detail that applies to their own route into Sweden — worth checking directly rather than assuming the rule is identical to whichever EU country you last checked.

