The 2010 Italian Open champion, who retired in 2015, had been suffering from cancer.
After a successful amateur career that saw him win the European Young Masters, Swedish Junior Stroke Play Championship and represent his country in the Eisenhower Trophy, he turned professional in 1992.
He claimed two wins on the Challenge Tour in 1993 and 2000 and spent most of the following decade on the European Tour.
“Fredrik was much loved in the golfing world and beyond, particularly amongst our Scandinavian players and staff, past and present,” said European Tour chief operating officer Keith Waters. “Our hearts go out to them at this incredibly sad time.”
Andersson Hed leaves behind wife Anna – whose surname, Hed, he added to his own when they married in 2004 – and children Viggo and Molly.