"There's a concern the potential health risk of this technology hasn't been investigated fully," says the union's general secretary, Philip Parkin.
The Health Protection Agency says "wi-fi devices are of very low power, much lower than mobile phones".
Mr Parkin, leader of the Professional Association of Teachers, is writing to Education Secretary Alan Johnson to ask for a "full scientific investigation into the effects of wi-fi networks in schools".
"I am concerned that so many wireless networks are being installed in schools and colleges without any understanding of the possible long-term consequences.
"I am not saying there is a danger, but I have enough concern to ask for it to be investigated."
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