Smith said Jenkins failed a field sobriety test after the accident Saturday, which followed torrential rain storms.
The bodies of three boys - ages 4, 7 and 11 - were found inside the vehicle.
Two girls ages 1 and 3 were missing.
"We have our helicopters flying over the bayou right now to see if they can find anything on the banks," he said. "But there's a lot of bayou out there."
The car crashed into a tributary about two miles from the point where it feeds into Greens Bayou, a waterway that begins in northern Harris County and flows eastward and then south for about 40 miles before emptying into the Houston Ship Channel. Smith said the bodies could be anywhere along the bayou.
The driver and another adult escaped from the vehicle, along with a 10-year-old girl.
It took 2 1/2 hours to find the car in the ditch, which had filled with 9 1/2 feet of fast-moving water.
Police said the vehicle was swept 100 feet from the spot where it left the road.
Police said the adult passenger, who is Jenkins' brother, told police Jenkins was the father of four of the children, including the 10-year-old girl who escaped. The other two children were believed to be family friends, Smith said.
Jenkins' brother told police rain was falling heavily when Jenkins answered a cell phone. He said Jenkins lost control when he hung up the phone and the car flew down an embankment into the ditch, Smith said.
At least one other traffic death was blamed on the powerful storms that swept across southeast Texas.
Smith did not know if Jenkins had an attorney to speak for him.
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