The perpetrators ordered electronic IDs from telecommunications giant TeliaSonera using the names of wealthy Swedes, business daily Dagens Industri reports.
An investigation is underway to ascertain how the scammers managed to get hold of registered letters sent to the victims.
Using the ill-gotten ID codes contained in the letters, the scammers targeted well-off customers with Avanza Bank and state mortgage lender SBAB.
Police suspect the thieves may have had help from an insider, either at the postal service or at a postal collection point.
Alternatively, the fraudsters may have accessed the victims’ letter boxes and picked up their mail at a registered postal outlet using fake ID.
"I’m not going to release any names but I regard them as well-known,” said prosecutor Jonas Svanfeldt, who is leading the preliminary investigation.
The investigation is just a few days old and has the potential to swell.
"We received indications around a week ago from banks and the police," TeliaSonera's press officer, Hans G Larsson, told the TT news agency.