Concerns were raised after the youngster drew a picture of a man cutting the vegetable.
Staff in Luton told the child's mother they believed he was saying "cooker bomb" instead of "cucumber".
The case was sent to a police and social services panel instead of de-radicalisation scheme Channel.
It decided not to take further action.
The boy's mother, who has not been named to protect her son's identity, concluded the confusion was due to the way her son pronounced the word.
"She (the member of nursery staff) kept saying it was this one picture of the man cutting the cucumber....which she said to me is a 'cooker bomb', and I was baffled," she told the BBC Asian Network.
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She said she feared her children would be taken away from her and added: 'But I haven't done anything wrong... It was a horrible day."
Teachers and public service workers have a legal obligation to report any concerns of extremist behaviour to the authorities since July.
Just under 2,000 under-15s were referred between January 2012 and December 2015.
Teaching unions say there is confusion over the government's counter-terrorism strategy in schools.
Alex Kenny from the National Union of Teachers said: "Teachers are scared of getting it wrong.
"They think Ofsted is going to criticise them if they haven't reported these things, and you end up [with] the boy making the spelling mistake, or the boy saying something in Arabic - that then gets reported on."
The Department for Education said its counter-terrorism strategy Prevent is "entirely consistent" with schools' responsibilities and "good schools would already be safeguarding children from extremism".

The exotic pet, which is 12 months old, has a vulnerable shell and the shop appealed for information on Facebook, saying it was concerned about its "specific care requirements".
The animal was taken from Lathom Pets and Aquatics in Ormskirk on Tuesday afternoon, Lancashire Police said.
The shop's owner said CCTV showed a man taking the tortoise - which needs calcium supplements - out of the tank.
Four people had entered the pet shop together, co-owner Catherine Broxholme said.
"I was serving, chatting to the group and getting change out of the till for a woman I was serving. The tortoise tank is just a few feet away from the till. We only have five tortoises and when I checked later there were only four."
CCTV footage confirmed a man had taken the tortoise, she said.
Ms Broxholme said she was concerned for the exotic pet's welfare, adding: "They have specific care needs. We are a welfare-oriented pet shop, making sure the pets go to good homes.
"The tortoise is about 12 months old and its shell is still vulnerable and it needs calcium supplements. We just want to get the tortoise back safe."
Police said the tortoise was valued at Â£120.
A nursery suggested referring a four-year-old boy to a de-radicalisation programme after he mispronounced the word "cucumber", it is alleged.
[NEXT_CONCEPT]
A baby tortoise has been stolen from a pet shop in Lancashire.