Another soldier was in "very serious" condition after the Friday blast in Mazar-e-Sharif, while the other two suffered minor injuries, the Swedish Armed Forces said in a statement.
"It is with deep sorrow I am forced to state that a Swedish solider has been killed," Supreme Commander Hakan Syren said.
Two civilians were injured in the attack, officials in Afghanistan said.
Stockholm has about 90 military personnel in the 12,000-strong force, and the government recently said it would double its peacekeeping force in Afghanistan, reported AP. P.T.
Russian small missile ships - the Grad Sviyazhsk and the Great Ustyug - set off for a mission to the Mediterranean Sea