It happened around 2:45 a.m. near FM 2920.
The woman, later identified as Erika Long, 28, had passed an 18-wheeler at a high rate of speed when she encountered a curve and lost control of her car, according to Sean Teare with the Harris County District Attorney's Office.
The car burst into flames when it crashed into a cable barrier in the median. A truck driver stopped to help the two as fire consumed the vehicle, deputies said.
The child was taken to UTMB Galveston with severe burns and was in critical condition.
Long was charged with intoxication assault with a vehicle and was in custody, according to court records. She had been treated for injuries at Memorial Hermann Hospital after the crash.
"The first officers on scene got to talk to her. She admitted she was drinking at a residence prior to this," Teare said. "When you think about what life this child has had for his 6 years on the planet, it's pretty tragic."
Saturday's arrest wasn't the first time Long had been accused of driving while intoxicated with children in the car, according to court records.
In 2015, Long was charged with DWI with a child under 15-years-old in Montgomery County. She was sentenced to six months in jail.
When the crash happened, she was free on bond on a pending theft charge.