The youngster’s family have asked that teachers at the Accrington school apologise for reporting the boy to the police after the mistake in an English lesson last month.
His cousin, who has not been named, told the BBC: “You can imagine it happening to a 30-year-old man, but not to a young child.
“If the teacher had any concerns it should have been about his spelling.
“They shouldn’t be putting a child through this. He’s now scared of writing, using his imagination.”
She added that she initially thought the incident had been a joke but police turned up at their home and examined the family’s lap-top.
A spokeswoman for Lancashire Police said: “This was reported to the police but was dealt with by a joint visit by a PC from the division and social services, not by anyone from Prevent.
“There were not thought to be any areas for concern and no further action was required by any agency.”
Since July teachers have been obliged to report any suspected extremist behaviour to police as part of the Government’s Prevent anti-radicalisation strategy.
The Department for Education issued advice for schools and childcare providers on how to meet the new requirement, saying: “It is important to emphasise that the Prevent duty is not intended to stop pupils debating controversial issues.
“On the contrary, schools should provide a safe space in which children, young people and staff can understand the risks associated with terrorism and develop the knowledge and skills to be able to challenge extremist arguments.”
Schools are expected to assess the risk of children being drawn into terrorism, including support for extremist ideas that are “part of terrorist ideology”.