Most Rev Justin Welby was accused by the National Secular Society (NSS) of using a speech in the House of Lords to "attack" non-religious schools.
The organisation said: "In attacking secular schools over their 'lack of values' yesterday, it appears the Archbishop of Canterbury was channelling Hitler!"
Adolf Hitler's Nazi Germany was responsible for the systematic murders of six million European Jews during the Holocaust. Homosexuals, political opponents and ethnic minorities were among other groups targeted in the killings.
The NSS compared Archbishop Justin's comments with a quote from Adolf Hitler in 1933, when the Nazi Party leader said "secular schools can never be tolerated".
During his speech on Friday, the Anglican leader suggested that non-religious schools fail to instil in pupils the values needed to help them challenge Utilitarianism in the world.
Opening a debate on the 'role of education in building a flourishing and skilled society', Archbishop Justin said: "We have a world of unguided and competing narratives, where the only common factor is the inviolability of personal choice.
"This means that, for schools that are not of a religious character, confidence in any personal sense of ultimate values has diminished.
"Utilitarianism rules."
In response, NSS chief executive officer Stephen Evans said: "Welby is absolutely wrong to attack community schools over their lack of transmission of values.
"Non-faith-based schools actively promote the same universal values as church schools.
"By promoting these values as uniquely "Christian", it's church schools that give their pupils a skewed and very poor understanding of ethics.
"The way in which the Church is increasingly using the state funded schools it runs to intensively promote its faith also undermines young people's religious and intellectual freedom."