The disaster occurred on Table Rock Lake outside the tourist city of Branson when a microburst storm hit the region, with winds of up to 75mph.
Governor Michael Parson stated he had spoken to a woman who had “lost nine of the 11 members of her family”.
The identities of the deceased individuals have not yet been confirmed.
However one of the two members of the family who did manage to survive was named as Tia Coleman by Fox59 News.
Commenting on the tragedy, Ms Coleman said: “I lost all my children, I lost my husband, I lost my mother-in-law, I lost my father-in-law, I lost my uncle, I lost my sister-in-law – she was my sister – and I lost my nephew, I’m OK, but this is really hard.”
She raised concern surrounding the safety of the boat tour, noting the captain had told the passengers not to put on life jackets during the storm.
She said: “The captain told us ‘Don’t worry about grabbing the life jackets, you won’t need them,’ so nobody grabbed them because we listened to the captain and he told us to stay seated.
“However in doing that, when it was time to grab them it was too late. I believe that a lot of people could have been spared.”
Another family member Carolyn Coleman stated two of her brother-in-laws had died in the accident.
She said the family had travelled to Missouri from Indiana earlier in the week for an annual road trip.
Commenting on the deaths, she told the New York Times: “We just lost some wonderful people.”
Officials said the incident occurred at around 7pm local time (0000 GMT) on Thursday as thunderstorms rolled through the area.
Governor Parson said seven of the 14 survivors were injured, with one seriously injured.
Commenting on the rescue operation, he said: “Emergency responders and civilian rescuers helped avert an even worse tragedy as people rushed to help in extremely dangerous conditions.”
A National Weather Service station in Springfield, 40 miles from Branson, issued a severe thunderstorm watch on Thursday evening shortly before the incident, with possible wind speeds of up to 75mph.
Michael Homan, a local resident, commented on the conditions to the New York Times, stating: “The wind picked up, they gave the storm warning.
“Then massive, straight line winds came out of nowhere.”
Jeff Raberding, a weather service meteorologist, added: “We knew there was going to be the potential for severe weather and knew that in advance.”
The president of Ripley Entertainment, the company which owns the duck boat tour company, admitted that the boats “should not have been in the water” in the weather conditions.
Speaking to CBS, he said: “I don’t have all the details, but to answer your question, no, it shouldn’t have been in the water if, if what happened, happened.
“Usually the lake is very placid, and it’s not a long tour.
“They go in and kind of around an island and back, and we had other boats in the water earlier, and it had been a very sort of calm experience up until this came very suddenly.”