Are deposit in Islamic banks accepted or prohibited in Islam?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Profits given by Islamic banks are lawful while interests given by usury-taking banks are forbidden. The banks that deal with Riba (interest and or usury) fix the interests in advance, but the Islamic banks give different profits according to Mudhaarabah (profit-sharing)

Allah Says (what means): {….. But Allaah has permitted trade and has forbidden interest. ….} [Quran 2:275]

Here, we state that what is mentioned above is the ruling, but some banks do not comply with the Sharee'ah rulings completely. So, we advise you to ask some scholars in your place of residence when you want to deal with an Islamic bank.

Allah Knows best.