Hailey was walking to a friend's home in Springfield just before 5 p.m. Tuesday. Witnesses told investigators that a man in a gold, 2008 Ford Ranger drove down the street several times before abducting the child.
Wood was arrested late Tuesday inside a vehicle parked outside his small single-story home.
The Springfield School District said Wood is a coach and teacher's aide who supervises in-school suspensions at a school for students in kindergarten through eighth grade. Hailey did not attend that school, and Williams said the two apparently didn't know each other.
"There's no connection that we've been able to determine at this time between the victim and the suspect," he said.
Williams said police have no idea of a motive for the killing. He said the suspect has not talked to investigators since his arrest.
The suspect's father, Jim Wood of Ash Grove, Mo., told The Associated Press that the girl's disappearance was "a tragedy" but declined further comment.
About 30 Springfield police investigators along with an FBI evidence response team searched the area near Wood's home Wednesday morning, as well as a nearby coin-operated laundry.
A records search shows Wood had little criminal history. He pleaded guilty to possession of a controlled substance in 1990 in Greene County and was fined $100.
Springfield School District Superintendent Norm Ridder said in a statement Wednesday that Wood began working for the district in August 1998. He is a paraprofessional and coach at Pleasant View K-8 School. Ridder said Wood has been suspended since his arrest.
Hailey did not attend the school where Wood worked. She was a student at Westport Elementary School this year, and was at Bowerman Elementary School last year. Springfield, with 162,000 residents, is Missouri's third-largest city.
"Student and staff at three of our schools are coping with this situation," Ridder said. Additional counselors and police were on hand at all three schools.
Associated Press reporters Margaret Stafford in Kansas City, Mo., and Jim Suhr in St. Louis contributed to this report.