Bang Phlat district chief Lakhana Phakdinaruenat said the fire started in the kitchen of the Riverside 3 boat, which was docked near Krung Thon Bridge in the district, at about 6.15am due to cooking gas leakage.
The two injured persons were Busaba Chairasameekul, 44, whose face, arms and legs were burnt and Thoedsak Kijwat, 41, whose whole body was burnt.
Pol Col Thanathit Wongwairak, chief of the Boworn Mongkol police station, said Mrs Busaba, who is a cook, was turning on a gas oven whne a gas leakage caused the fire. Mr Thoedsak, who is a security guard, tried to rescue her.
Marine official Trairat Sarakhram said the fire was put out at about 7.40am and half of the restaurant boat was damaged.