The crash killed at least 146 people but one of the Swedes was among the survivors, the Swedish foreign ministry said.
The Spanish airline Spanair is wholly owned by Scandinavian carrier SAS.
“As far as we know, there were only two Swedish citizens on board. One person has been located in the hospital,” ministry spokeswoman Gufran Al-Nadaf told AFP, adding only that the person was “alive.”
“The second person hasn’t been located yet,” she said.
The Spanair MD-82 made an emergency landing just after taking off from Madrid-Barajas airport heading for Las Palmas in the Canary Islands, according to an airport authority spokesman. Spanish media said an engine caught fire as it took off.
Spanish national radio said at least 146 people had been killed.