The World War Two-style amphibious vehicle was filled with 31 passengers including children when a microburst storm hit Table Rock Lake outside the tourist city of Branson, Missouri, on Thursday. A video of the incident showed it battered by waves.
Wendy Doucey, an office manager at the Stone County sheriff's office, said divers had recovered the four bodies from the sunken duck boat. The vehicle was 80 feet (24 m) underwater.
"It's important that we find out for sure what events did occur," Missouri Governor Michael Parson said at a Friday morning news conference. "Today it's just still early."
The incident began around 7 p.m. (0000 GMT) on Thursday after thunderstorms rolled through the area when two duck boats were out on the lake, officials said. Both headed back to shore but only one made it.
"From what I understand there was life jackets in the duck," Stone County Sheriff Doug Rader told the press conference. He declined to answer questions about whether passengers on the duck had been wearing them.