Swedish airport authority Swedavia said the plane involved in the crash was a GippsAero GA8 Airvan, an Australian-made single-engine aircraft popular with parachutists.
Some of the parachutists were seen trying to jump off the plane just before it went down, witnesses told Swedish media.
"I heard a weird sound, which didn't sound normal. I looked up and saw a plane spinning like a top," witness Peter Larsson told the Dagens Nyheter newspaper. "At first, I thought it was an acrobatic flight, but we quickly realized that something was wrong."
Another witness told Swedish broadcaster SVT she heard a loud noise from above before she saw the plane going straight down and crashing into the island.
All those on board on board the plane were Swedish, the BBC reported.
Swedish Prime Minister Stefan Lofven expressed "great sadness" over the accident in a statement to Swedish news agency TT. He sent condolences to the families of the victims and said the government would stay in close touch with officials probing the crash "as it is important to investigate the cause".
The cause of the crash is under investigation.
The Associated Press contributed to this report.