Officers say a 60-year-old man was hurt after picking up an object from the ground which exploded.
The explosion took place just outside the Varby Gard subway station in Huddinge, a residential district that is part of greater Stockholm.
Police also said the man died at the hospital and that the woman was also taken to the hospital and had wounds on her face and both legs.
But police haven't confirmed the exact nature of the explosive device.
Police declined to confirm reports that the object was believed to be a hand grenade.
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According to a Swedish police report published a year ago, Sweden is the European country where criminal gangs use the most grenades, often from stocks from the former Yugoslavia.
"It is too early to say", Mr Olsson said.
Police cordoned off the station and the square outside as bomb squad experts moved in to investigate.
Police patrols will remain in the area throughout Sunday night and Monday, with the municipality offering crisis counseling to local residents.
Authorities said they did not think the blast was related to a terrorist attack.
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