The mother, Michelle Kehoe, and older son Sean underwent surgery, the state Division of Criminal Investigation said in a statement Monday night.
Buchanan County Attorney Allan VanderHart said 2-year-old Seth Kehoe was found dead near the minivan. He said the mother and boy suffered serious injuries but wouldn't disclose the nature of the injuries.
VanderHart said no charges have been filed and it was too early to consider anyone a suspect.
"The death needs to be investigated and it could have been any number of scenarios," he said. "It's just not possible at this point to say that we have any one scenario that we're ruling out."
Michelle Kehoe's husband, Eugene, called police Sunday night to report his wife and children had been missing since they left their Coralville home earlier in the day, VanderHart said. They were headed toward Sumner and never arrived.
On Monday morning, sheriff's deputies were called to a home near Littleton when Michelle Kehoe went to a house and told the residents that "the children were in danger," a state Division of Criminal Investigation statement said. The minivan was found near the house.
Littleton is about 70 miles north of Coralville.
The death came about 10 months after a car driven by Michelle Kehoe veered off the road and into the icy Iowa River on Dec. 14, 2007. Michelle Kehoe said she lost control of the car because her sons had distracted her. All were saved with help from bystanders.
VanderHart said he wasn't familiar with the earlier matter but didn't think it was connected to Monday's events.
"Whatever incident that entailed has no bearing on this investigation," he said.