A third soldier has mild injuries. All three are being brought to a hospital in Europe.
A memorial service was held in Mazar-i-Sharif on Sunday while at the military headquarters in Stockholm staff observed a minute’s silence in honour of the Swedish soldier who died in Afghanistan on Friday.
The soldier’s body will be brought home to Sweden “in the near future”, said the military.
The condition of the Swede who was being flown back to Europe on Sunday remained critical. The soldier was unconscious, according to the military’s group chief Jan Jonsson.
The army would not say which European country the soldier was being taken to, nor where other two soldiers would be treated. Relatives will be able to visit them, however.
The four Swedish troops were from the NATO-led ISAF, which was set up in 2001, and were part of a British provincial reconstruction team.
The explosion, caused by a remote controlled bomb, happened as the truck in which the peacekeepers were travelling passed as part of a four-vehicle patrol. It took place near the centre of the city, where a British ISAF soldier was killed in an ambush nearly a month ago.
The Swedish military is not revealing the names of the dead and injured soldiers since they are part of a secretive special strike force, SSG, and their identities are therefore subject to confidentiality regulations.
The fourth person injured is an interpreter, whose identity is also secret.