Christian Oliver, 51, whose real name is Christian Klepser and who starred in movies such as “Speed Racer” and “The Good German,” died on Thursday.
The owner and pilot of the plane also perished in the crash.
Among the dead were his daughters, Madita Klepser, 10, and Annik Klepser, 12, and the plane’s pilot and owner, Robert Sachs, police said.
Police said the single-engine plane had just taken off from Becquia, a tiny island popular with tourists and part of the Caribbean nation of St. Vincent and Grenadines, after midday Thursday.
It was bound for the island nation of St. Lucia 65 miles to the north.
Days earlier, Oliver had posted a picture of a sunset beach scene to his Instagram account wishing followers a happy new year “from somewhere in paradise.”
Local fishermen and divers rushed to the scene before the Coast Guard recovered four bodies, which were then pronounced dead.
The bodies were taken to a mortuary on St. Vincent where post-mortems will officially determine the cause of death.
The police force said it “expresses condolences to all who are negatively affected by this tragic incident.”