Instead, NATO jets were dispatched from Lithuania to shadow the Russian planes, The Local.se reported Monday.
A Swedish newspaper, Svenska Dagbladet, revealed Monday that Russian jets flew within 25 miles of the country's border during a Good Friday military exercise.
Two Swedish military planes used to identify foreign aircraft did not deploy, but two Danish F-16s attached to NATO were dispatched from Lithuania.
Members of the Swedish parliament slammed the military's lack of reaction to the incident.
Peter Hultqvist, a Social Democrat who heads the parliamentary committee on defense, called the lack of reaction by the Swedish military "exceptionally serious."
"We should be prepared any day of the year," he said.
Sweden is not a member of NATO, but a spokesman for the Swedish Liberal Party, Allan Widman, said the incident showed the country needed to increase its cooperation with other countries and 'become closer" to the organization.
Defense Minister Karin Enstrom said the fly-by demonstrated the Russian military had stepped up its training exercises and now "act in a different way."
Foreign Minister Carl Bildt was not alarmed by the Russian action.
"We don't react to everything, we're not up in the air for everything and we shouldn't be," he said, adding he did not plan to ask Russia for an explanation.
Danish Foreign Minister Nick Haekkerup said the F-16s "did exactly as they should have," but that the presence of the Russian jets was "not something we are used to seeking in these parts," The Copenhagen Post reported.