The Missouri State Highway Patrol said the explosion happened near Sunrise Beach. The boat was docked when a mechanical failure caused a fuel-related fire, the patrol said.
James and Kari Hohenstein, Brad Vanwinkle and two children aged 12 and 16 were seriously injured. The 16-year-old and Vanwinkle were flow to University Hospital in Columbia for treatment, while the three others were taken to a nearby hospital.
A 2-year-old was taken by private vehicle to the hospital with minor injuries.
The people on the boat are from Gretna and Elkhorn, Nebraska.