Two priceless crowns and an orb belonging to a 17th Century king and queen were taken at around midday on Tuesday in Strängnäs, near Stockholm.
Witnesses said they saw two men running from the cathedral, which was open to the public and hosting a lunch fair.
They were seen motoring off into Lake Malaren, and have not been seen since.
Police have launched a huge search operation, but currently have no suspects.
“It’s 1-0 to them right now,” police spokesperson Thomas Agnevik told Swedish media. “It is not possible to put an economic value on this, it is invaluable items of national interest.”