Reference: Silsilah Kitaab ad-Da’wah (1), al-Fataawa – Volume 1, Page 147
Question: Is it permissible for whoever has a lump sum of money to put it in a bank with the intention for safe keeping, and whenever the zakaah is obligatory upon that sum of money he extracts the required amount and gives the zakaah? Please advise us, and may Allaah reward you with good.
Response: It is not permissible to deposit money for safe keeping in a bank which deals with ribaa, even if you do not take the ribaa, since this entails assisting in sin and transgression, and Allaah has forbidden that.
However, if you are compelled to do so, and do not take the ribaa, and you are unable to find another place to safe keep your money except a bank which deals with ribaa, then there is no harm due to the necessity, in shaa.-Allaah. And Allaah (Subhaanahu wa Ta’aala) says:
{He has explained to you in detail what is forbidden to you, except under compulsion of necessity}, [Soorah al-An’aam, Aayah 119].
And whenever you find an Islaamic bank or a safe place which does not involve assisting in sin and transgression, then place your money there, as it will not then be permissible for you to leave [your money] in a bank which deals with ribaa.