The Palestinians cheered Thursday's move, while Israel summoned Sweden's ambassador to protest and express disappointment.
Foreign Minister Margot Wallstrom said in a statement that the recognition was "an important step that confirms the Palestinians' right to self-determination".
"We hope that this will show the way for others," she said in remarks published in the Dagens Nyheter daily.
Palestinian President Mahmoud Abbas hailed the "brave and historic" move to officially recognise the state of Palestine, his spokesman told the AFP news agency.
Sweden is the first EU member state in Western Europe to recognise the Palestinian state.
Seven EU members in eastern European and the Mediterranean have already recognised a Palestinian state - Bulgaria, Cyprus, the Czech Republic, Hungary, Malta, Poland, and Romania.
Non-EU member Iceland is the only other western European nation to have done so, AFP reported.