It is not permissible to put money in a bank that deals in riba (usury or interest), and the Muslim should not do that unless he is forced to, in which case the following three conditions apply:
1 – He should have the need to do that, meaning that there is no safe place to keep his money except this bank. If he can find another place where he can keep his money apart from this riba-based bank, then it is not permissible for him to deposit his money in this bank which deals with riba.
2 – The bank should not deal one hundred percent with riba; if the bank’s dealings are one hundred percent with riba then it is not permissible to deposit his money with them at all, if you deposit money in the bank then in this case you can be certain that you have helped the bank engage in riba, and it is not permissible to help anyone with riba.
3 – The depositor should not take any profit, because if he takes any profit that will be riba, and riba is haraam according to the Qur’an and Sunnah and the consensus of the Muslims.
With regard to the questioner’s saying that if he does not take the interest the bank will take it:
This is not interest, rather it is riba which is haraam, and it belongs to the bank in the first place. The depositor does not have the right to take anything of it, because Allaah has commanded us to abstain from riba when He said (interpretation of the meaning):
“O you who believe! Be afraid of Allaah and give up what remains (due to you) from Ribaa (from now onward) if you are (really) believers”
And He warned against taking riba when He said:
“And if you do not do it, then take a notice of war from Allaah and His Messenger”
It should also be noted that depositing this money in the banks is not regarded as depositing it in the shar’i sense, because depositing something in sharee’ah means leaving it with someone for safekeeping, which means that the owner cannot use it; but when money is deposited in the bank, the bank uses the money, so it is a form of lending, not depositing for safekeeping. The fuqaha’ have explained this point, that if the depositor gives the keeper permission to use his money, it is no longer a deposit for safekeeping, rather it is a loan. (Therefore anything added to the principle is riba).
And Allaah knows best. May Allaah send blessings and peace upon our Prophet Muhammad.
See Fataawa Manaar al-Islam, 2/433-440 by Shaykh Ibn ‘Uthaymeen.