The man, who is in his 20s, was held on a bus en route to Germany with 19 guns in his suitcase, Swedish public broadcaster SVT and Albanian media report.
According to Albanian police the weapons were found during a routine check.
“What we can say is that we are aware of reports that a Swedish man has been arrested on the border between Albania and Montenegro,” foreign ministry spokesperson Magdalena Nergården told SVT.
“According to the information we have he is suspected of weapon smuggling and Sweden's embassy in Tirana is monitoring the case,” she added.
Albanian police say on their website that they have tightened border controls to stop weapon and drug smugglers by using specially trained dogs to search through luggage.