Lindh, 46, who had been tipped as a future prime minister - as well as being a leading campaigner for Sweden to join the European Union's single currency in Sunday's referendum - was stabbed repeatedly in a Stockholm department store.
"Her family has lost a mother and a wife. Social Democracy has lost one of its most gifted politicians. The government has lost a skilled politician and a good colleague. Sweden has lost its face towards the world," said Prime Minister Goran Persson.
Tributes to one of Sweden's most popular politicians had poured in from all over Europe as surgeons at Stockholm's Karolinska hospital struggled all night to save her life.
"It is horrible and incomprehensible. Sweden has lost a great politician and a fantastic foreign minister"
But on Thursday the hospital issued a statement saying that Lindh had died of "massive bleeding caused by knife wounds to the liver and many of the big blood vessels in the abdomen".
The stabbing took place in the final days of campaigning for the referendum, but it was not clear whether they were linked.
Politicians were to meet at noon (1000 GMT) to decide whether the referendum should go ahead. Lindh had campaigned for the pro-euro side, which has trailed opponents in opinion polls.
Ordinary Swedes left red roses at the hospital and the store where she was killed, shocked at the first political killing in their country since the unsolved assassination of Prime Minister Olof Palme in a Stockholm street in 1986.
Except for Persson, politicians in Sweden rarely have bodyguards to ensure they keep close to the electorate - a policy now likely to be reviewed across the Nordic region.
Persson called the stabbing "an attack on our open society" and urgently ordered increased security around King Carl XVI Gustaf, top politicians and major public buildings.
Doctors were unable to save Lindh
Police scoured the country for Lindh's killer, described only as tall and "Swedish looking", who dumped his army jacket and knife near the scene of the attack in central Stockholm. Store video footage was being scanned for clues to his identity.
"It is horrible and incomprehensible," said Maud Olofsson, head of the opposition Centre Party. "Sweden has lost a great politician and a fantastic foreign minister."
Lindh was a forceful voice on human rights who dubbed US President George W Bush a "lone ranger" for going to war in Iraq. She criticized Italy's current EU presidency, saying Prime Minister Silvio Berlusconi did not enjoy wide support.
Married with two children, she became foreign minister in 1998 after a stellar career in the Social Democratic Party which has ruled Sweden for six of the last seven decades.