The accident happened in the southern state near Moore Haven city on a major US highway.
Officials said the van "passed through a posted stop sign and traveled across all lanes of US 27.
"The van then traveled into a steep partially water-filled canal," Lieutenant Gregory Bueno of Florida Highway Patrol said in a statement to AFP.
There were 18 people in the vehicle at the time of the accident and no other cars were involved, Bueno said.
One of the 10 injured is in a serious condition in hospital. A four-year-old boy is in a stable condition.
Florida Highway Patrol said they were investigating the accident.