The Solna team released a statement to say Turina died at home in his sleep on Wednesday night and there are no suspicious circumstances surrounding his death.
"It is with great sorrow and shock that AIK can confirm goalkeeper Ivan Turina died during the night between Wednesday and Thursday," it read.
"AIK's thoughts are with Ivan's wife and two daughters, as well as his other relatives and friends.
"AIK have informed the players about what has happened. We ask people to respect everyone concerned and allow them the chance to grieve in peace."
Reports in the Swedish press say Croatian Turina had previously suffered from heart problems.
Turina joined AIK in the summer of 2012 from Dinamo Zagreb in his homeland and made 89 appearances for the Allsvenska club.