I would like to know what Islam says about depositing money in an Islamic bank. Is it considered as "Riba"?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

It is allowed to deposit your money in Islamic banks. On the opposite side, it is Haram to deposit your money in usury-taking-bank since this action constitutes a form of co-operation in sin.
Allah Says (interpretation of meaning): {… Help you one another in AlBirr and AtTaqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. …} [5: 2].
But, if there are no Islamic banks where you are living and you are afraid that you may lose your money, then it is allowed to deposit your money in a current account in a usury-taking-bank to the extent of need.
Here, you have to spend any interests you receive on behalf of the public interests of Muslims, although it is safer to avoid dealing with such banks, i.e. usury-taking-banks.
Allah knows best.