Teachers in England taking initial teacher-training courses and postgraduate certificates of education say they have been urged to use the phrases "word-storm" or "thought-shower" instead.
Charities who work with epileptic children have attacked the ban as needless political correctness.
One newly-qualified secondary school teacher said she was irritated at being warned against using the word, even though her mother suffered from a brain tumour and had seizures as a side-effect.
"When I started my PGCE, I didn't have a problem with the term 'brainstorm'
- even though, clearly, epileptic fits hold some very nasty connotations for me," she said.
"Now, however, because of people banging on about it being offensive, I would advise teachers to stick with brainstorm or use thought-shower, but not to make a fuss about it."
The National Society for Epilepsy has also received reports that teachers are being asked to avoid the word. Margaret Thomas, its head of communications, conducted a survey of people with epilepsy to gauge their reactions.
"The overwhelming response was that 'brainstorming' implies no offence to people with epilepsy, and that any implication that the word is offensive to people with the condition is taking political correctness too far," she said.
She added that words people with epilepsy did find offensive included "fit", as they preferred the term "seizure".
The National Centre for Young People with Epilepsy said that its staff often used "brainstorming" sessions when working with pupils.
In the United States, birthplace of political correctness, Brainstorm is the name of an epilepsy-awareness campaign teddy bear.