The call from the Educational Institute of Scotland (EIS), Scotland's largest teaching union, follows a survey of councils that showed many no longer have specific anti-racism education policies.
Of the 24 local authorities that responded to the EIS inquiry, 17 had no dedicated policies on the issue at all.
Larry Flanagan, general secretary of the EIS, said he was "genuinely concerned" at the inconsistent approaches to anti-racist education adopted across the country.
He said that because Scotland was a multi-ethnic country with a sizeable migrant population, it was vital all pupils were taught about issues of racism.
He said: "With the worrying rise of the far-right in some parts of the UK, together with the ideologically-driven demonisation of many migrant groups by some politicians, it is essential we take appropriate steps to educate all our young people on anti-racism while highlighting the cultural value of the diverse ethnic mix that exists throughout Scotland.
"While some authorities have well-developed policies, others have no specific anti-racist education policy or consider this area of work within other existing strategies, such as anti-bullying policy.
"The EIS believes anti-racist education should permeate the curriculum in all learning establishments and should be seen as a fundamental part of the learning and teaching process.
"Young people in schools must grow up learning that we are all part of a multi-ethnic society and it is essential that all schools provide education on this topic in order to develop positive values and behaviour."
Douglas Chapman, education spokesman for council umbrella body Cosla, said: "Racist behaviour in all its forms is not tolerated and is treated extremely seriously. Local authorities and schools have policies in place to deal with a range of serious incidents including racist behaviour in and around the school.
"We should never be complacent when it comes to racism, and I share the EIS's abhorrence for ignorance and bigotry, but I'm not convinced that calling for anti-racist education to be made a requirement in all Scottish schools is the right way to go."
A spokesman for the Scottish Government said racism and racist bullying would not be tolerated in any schools.
He said: "We expect councils and schools to tackle racist behaviour where it does occur. Under Curriculum for Excellence, pupils will learn about different cultures and beliefs to develop them as informed and responsible global citizens with a knowledge of Scotland and its place in the world.
"Racism can be addressed across the curriculum for example in expressive arts, health and wellbeing, literacy and English, religious and moral education and social studies.
"Education Scotland have a number of useful resources available for teachers on their website on tackling the issue of racism in schools in Scotland."
Nearly 88,000 racist incidents were recorded in Britain's schools between 2007 and 2011, according to figures released earlier this year.