Beaumont police on Wednesday identified the mother as 41-year-old Colette Sulcer and said her daughter was being treated for hypothermia but doing well.
Capt. Brad Penisson of the fire-rescue department in Beaumont said the woman's vehicle got stuck Tuesday afternoon in the flooded parking lot of an office park just off Interstate 10. Squalls from Harvey were pounding Beaumont with up to 2 inches (5 centimeters) of rain an hour at the time with 38 mph (60 kph) gusts, according to the National Weather Service.
Penisson said a witness saw the woman take her daughter and try to walk to safety when the swift current of a flooded drainage canal next to the parking lot swept them both away.
The child was holding onto the floating woman when a police and fire-rescue team in a boat caught up to them a half-mile downstream, he said. Rescuers pulled them into the boat just before they would have gone under a railroad trestle where the water was so high that the boat could not have followed. First responders lifted the child from her mother's body and tried to revive the woman, but she never regained consciousness.
The child was taken to the Christus St. Elizabeth Hospital in Beaumont, and was expected to be released Wednesday. Officer Carol Riley said the girl was doing "very well" and was chatty.
"Everybody at the hospital and the officers just fell in love with her," Riley said.
At least 20 people have been killed by Harvey since Friday, when it made landfall in Texas as a Category 4 hurricane. Harvey has since weakened to a tropical storm.
A Gofundme page set up to help the child has surpassed it's $100,000 goal.