A six-year-old Muslim boy with Down's Syndrome was probed for terrorism after his teacher called the police alleging that the boy kept repeating the words "Allah" and "boom" in class.

Mohammad Suleiman has intellectual difficulties and doesn't speak, his father Maher Suleiman told the Fox26 news channel.

Maher said Mohammad attends C J Harris Elementary School in Pearland near Houston and the teacher who called the police was covering for a regular member of the staff at the school.

Mohammad's parents dismissed the school's claim because "he doesn't speak at all", and has "the mental capacity of a one-year-old".

Maher said the family has been through a rough patch since they have been questioned by both the police as well as the Child Protective Services (CPS).

"The last three or four weeks have been the hardest of my life," Maher told the news channel. "My wife and kids were crying a few days ago and I told them everything is fine.

"Mohammad was born with Down's Syndrome Chromosome 21. He needs care all the time. They claim that he's a terrorist. This is so stupid, this is discrimination actually. It's not implied discrimination, it's a hundred per cent discrimination," he added.

Quanell X, a community activist, told the channel: "In my opinion, based on everything I heard from the police department and speaking with the administration from the school, this was a story piecemealed together by a substitute teacher alleging this child was sexually harassing her, the teacher, and possibly being a terrorist."

The Pearland Police Department said they conducted an investigation but nothing was found that needed police involvement, the channel reported.

CPS said its investigation remains open.

A spokesperson for the Pearland Independent School District said they cannot release any student or personnel information due to privacy laws.