Muslim women do get breast cancer, but figures from cancer registries in the Britain show that women of South Asian origin (that is, women who were born in, or whose families come from, Pakistan, India or Bangladesh) do have a lower risk of getting breast cancer than other women in the UK. 

Overall the risk is about one third less.  This means that for every 100 women in the UK, 9 will get breast cancer at sometime during their life, whereas for women of South Asian origin the figure drops to 7 out of every 100. 

The cancer registry figures have looked at the effect of religion and show that this reduced risk is the same for all women from South Asia, be they Muslim, Sikh, Hindu or of other faiths.  So it is the ethnic origin, rather than religious belief, that seems to be the important thing in reducing the risk of breast cancer for women from South Asia.