MSHP said there was a mechanical problem that caused a fuel-related fire.
Three adults on the boat were taken to local hospitals with serious injuries. A 16-year-old and 12-year-old also suffered serious injuries and were transported to local hospitals.
A 2-year-old on the boat was hospitalized with minor injuries, the MSHP report said.
All passengers on the boat are listed as being from Elk Horn or Gretna, Nebraska, more than 300 miles away.
Lake of the Ozarks is a popular summer vacation spot in the Midwest, with more than 1,100 miles of shoreline.