There is no minimum credit score required by the Federal Housing Administration to be able to get a loan! But there is a minimum credit score required by the lenders that underwrite, close and fund these types of loans.
This is called a Lender Overlay and all lenders have them. Basically the statistical data available show that borrowers with credit scores below 640 have a much higher likelihood of going into default causing the bank to foreclose. So as a general practice lenders have set their minimum credit score to be able to get a FHA loan at 640.