A car blew up in a busy shopping area on Saturday afternoon, followed moments later by a second explosion nearby.
Witnesses said a man found dead after the second blast had been carrying an explosive device. Two people were hurt.
Swedish PM Fredrik Reinfeldt condemned the attacks as unacceptable in an open society with a functioning democracy that respects different cultures.
"Our democracy functions well," he told a press conference. "Those who feel frustration or anger have the opportunity to express it without resorting to violence."
Police are investigating a set of e-mails sent shortly before the blasts threatening attacks because Sweden had sent troops to Afghanistan.Sweden has some 500 soldiers deployed in Afghanistan as part of the international military force.
Police are trying to work out whether the explosions were an isolated attack or part of a larger conspiracy, says the BBC's Stephen Evans in Stockholm.
Sweden has a reputation for openness and tolerance, but in recent years, tensions have risen, our correspondent says.
There has been resentment at immigration as the economy has stuttered, and Muslims have grown more militant.
The e-mails, with MP3 audio files in Swedish and Arabic, were sent to the Swedish security service and the TT news agency.
They called for "mujahideen" - or Islamist fighters - to rise up in Sweden and Europe, promising Swedes would "die like our brothers and sisters".
They also attacked the country for caricatures of the Prophet Muhammad drawn by Swedish artist Lars Vilks.
