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.
Swedish police could not immediately confirm the death.
The blast took place at about 11am on Sunday, just outside the Varby Gard underground station in Huddinge, a residential district in greater Stockholm, said regional police spokesman Sven-Erik Olsson.
Police said the apparent attack was not aimed at these two people.More news: $50000 Winning Powerball Ticket Sold in Wilkes County
"The man was seriously injured after he picked up something from the ground and this device exploded", Mr Olsson said. "I don't dare imagine what would have happened if one or several children had found the hand grenade".
Daily newspaper Aftonbladet said it was thought to have been a hand grenade.
The Varby Gard station, on the Red Line in southwest Stockholm, has been closed off for investigation.
Police cordoned off the station and the square outside as bomb squad experts moved in to investigate.