"It is with great sorrow and shock that we can confirm that goalkeeper Ivan Turina passed away on the night between Wednesday and Thursday," the club said in a statement.
"Ivan died suddenly in his sleep and at the moment no crime is suspected."
Croatian Turina, the father of one-year-old twins, was known to have a congenital heart problem which he told the club about when he signed for them in 2010.
"We knew that he had a congenital heart problem but he was completely healthy," AIK chairman Johan Segui told newspaper Expressen.
Striker Henok Goitom, who lived next door to Turina, said he had been summoned by the family. "His wife's mother rang hysterically on my doorbell," he told reporters at the team's Karlberg training ground.
"Yesterday was an ordinary day. Today, Ivan is dead," he said. "It's a shock. The AIK supporters loved him. It's a slap in the face for everyone but we are united as a group and we're trying to help everyone in AIK and his family."
Turina's wife is expecting the couple's third child.
Fans streamed to Karlberg to lay scarves and flowers at an impromptu shrine to the popular keeper, who had recently extended his contract with the club to 2016.
Flags at the training ground flew at half mast as red-eyed players and staff spoke quietly with the assembled media and supporters.
Turina played 89 competitive matches for the club, keeping 35 clean sheets, and he won a single cap for Croatia when he played against Hong Kong in 2006.
It was unclear whether AIK's next league game against IFK Gothenburg on Monday would go ahead as planned.
- Sports & Recreation
- Ivan Turina