Highfield School in Ossett, which caters for children with special education needs, sent the message to set up the regular weekly transport arrangement with a taxi company.
But because of the complex needs of some of its pupils, the request stated that the passenger “will not tolerate anybody who is not white British”.
Peter Marshall, executive headteacher of the school, said: “We fully acknowledge that the email sent by the school was wholly inappropriate and we apologise for any offence that was caused.
“Our priority is to support our pupils, many of whom have extremely challenging and complex needs.
“Over 180 children from our school community use minibuses and taxis to enable them to access the highly-specialised teaching and care we are able to provide for them.
“We very much value and appreciate the service that all taxi companies and their drivers provide.
“We have contacted the taxi company to apologise and explain the challenges and needs faced by the pupil the request related to.”
Wajid Ali, co-chairman of Wakefield District Private Hire and Hackney Association, said: “We try to promote equality and diversity and our drivers work very hard to keep professional standards.
“The majority of taxi drivers are Asian, but race or colour should not come in to it.
“This is the first instance something like this has come to light and everybody is very angry about it.
“It’s like going back 50 years. We are not living in a draconian era.”