Praise be to Allah.
If these banks really operate according to Islamic sharee’ah, and they do not deal with riba which is haram, and they do not take what is called interest in return for deferring payment, which is in fact the riba (usury) of the Jaahiliyyah, even if they call it by some other name, and they do not engage in transactions which are not acceptable in sharee’ah, such as selling what one does not possess, or ‘aynah sales or other kinds of transactions that are not permitted by sharee’ah – then undoubtedly a bank that does not do these things is halal and dealing with it is acceptable according to sharee’ah.
But if these banks are Islamic in name only and they deal with riba and other forbidden transactions, then dealing with them is haram, even if they call themselves “Islamic banks”, because what counts is what really happens, not mere names.
The Standing Committee for Issuing Fatwas was asked: Is it permissible to deal with Islamic banks, even though some of them go against sharee’ah and engage in kinds of transactions that are forbidden?
It is permissible to deal with banks and financial institutions that do not deal with riba. But if they deal with riba then it is not permissible to deal with them, and they are not Islamic banks.
Fatawa al-Lajnah al-Daa’imah, 13/310.
And it also says in Fatawa al-Lajnah (13/365):
If the Islamic bank does not deal with riba, and rather it invests money according to shar’i principles, then it is permissible for you to deposit your money with them for investment purposes.