The boy was seen dragging the younger boy from outside his home, near Vos Street and Walnut Avenue, until the victim's stepmother came out to help.
"The suspect used a rouse to get the 6-year-old from the yard and then physically removed him from the area," said Lt. Mark Bennett of the Ottawa County Sheriff's Department.
The victim's stepmother said the two children shared a class at Pinewood Elementary School for students with behavioral problems. She was notified of the alleged abduction by a school bus driver who saw both of them struggling.
"When she found them, she had trouble getting the 6-year-old away from him," Bennett said. "She had to forcibly remove the young man."
Investigators said they've responded to incidents involving the older boy in the past.
The younger boy was not injured in the incident, police said, and he returned to school on Friday.
The 11-year-old is being held at the county juvenile detention facility and is expected to have a hearing next week.