Members of Pink Floyd, who received the annual prize along with American soprano Renee Fleming, sat in the crowd as Reinfeldt sang 'We don't need no education', capping his one-line performance with an emphatic 'Yeah'
"If the Prime Minister decides to sing for the people of Sweden I wish he would least choose to sing lyrics that did not proclaim our lack of a need for education," union chairwoman Metta Fjelkner said in a statement.
The head of the National Union of Teachers (Lärarnas Riksförbund) added that the Prime Minister should try to make up for his anti-educational crooning by singing something positive about "a profession he calls the most important in the country."
Education Minister Jan Björklund refused to be drawn into a serious debate when quizzed on TV4 about the reaction of the teachers union.
"We're going to have to call an extraordinary government meeting," he laughed.