Kalla and Ingemarsdotter were beaten by US duo Jessica Diggins and Kikkan Randall, who crossed the finish line in 20:24.44.
The Swedes came in 7.80 seconds later, with Finland's Riikka Sarasoja-Lilja and Krista Lahteenmaki taking bronze.
In the men's event, Russian duo Alexey Petukhov and Nikita Kriukov claimed the gold, crossing the finishing line at 21:30.98.
Kriukov sprinted past Jönsson in the home stretch and Hellner could not keep up the pace with Petukhov.
But the Swedish men came in second, before Kazakhstan's Nikolay Chebotko and Alexey Poltoranin, who picked up bronze.
The Swedes were pleased with their performances.
"Straight after crossing the finishing lines I had mixed feelings, but deep inside I was really happy we got a medal," Jönsson told Sveriges Television (SVT).
Kalla and Ingemarsdotter who won gold in the 2011 World Championships called Sunday's competition "a tough day at work".
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"We should be really pleased with ourselves. We won a medal," said Ingemarsdotter.
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