Twenty-two people were killed and 59 injured when an as-yet unnamed man detonated a bomb at a concert of the US popstar, who is popular among teenagers and children.
This is a brutal and senseless attack which wounds every decent person in their heart."
"We mourn the dead, and we think of the families whose loved ones will never come home," Löfven added in a statement published on the Swedish government's website. "Sweden shares the British people's shock and anger."
The attack has thrown a shadow over tomorrow's Europa League final in Stockholm, which is expected to bring thousands of Manchester United fans to the city.
Anna Kinberg Batra, leader of Sweden's opposition Moderate party, said the bombing was "a terrible attack on the whole of our society".
Manchester United is set to play Amsterdam's Ajax in the Friends Arena stadium on Wednesday.
"We are deeply shocked by last night's terrible events at the Manchester Arena," Manchester United said on its Twitter feed. "Our thoughts and prayers go out to all those affected."
According to the UK's Daily Mirror newspaper, players are expected wear black armbands during the match, which kicks off at 8:45pm.
Some 9,500 fans have been allocated tickets for the final, and thousands of ticketless fans are also expected to come to Stockholm.
The Swedish Football Federation is putting up a giant screen at Kungsträdgården, a park in the centre of Stockholm.