Eyewitnesses said the park's Jetline roller coaster had partly derailed during a ride, sending people crashing to the ground.
"This is tragic and shocking, and regrettably we've learned that one person has died," Grona Lund spokeswoman Annika Troselius told public broadcaster SVT.
Ambulances, fire trucks and a helicopter were seen arriving at the park, and police launched an investigation.
Police said nine people were being treated in hospital, including three who had severe injuries.
Grona Lund said in a statement the 140-year-old park was closed until further notice.Â
Jenny Lagerstedt, a journalist visiting the park with her family, told SVT she was nearby and heard a metallic noise and noticed the track structure was shaking at the time of the accident.
"My husband saw a roller-coaster car with people in it falling to the ground," Lagerstedt said.
"My children were scared," she added.
The steel-tracked Jetline roller coaster reaches a speed of up to 90 km/h and a height of 30 metres, transporting more than one million visitors each year, the amusement park says on its website.
Sweden's Culture Minister Parisa Liljestrand said news of the accident was incomprehensible.
"My thoughts are with those that were affected as well as their families and loved ones," Liljestrand said in a statement to the TT news agency.
