The plea follows a number of churches and other religious institutions that have been closed down in recent months.
The UNHRC urged Algeria to "guarantee the full exercise of their freedom of thought, conscience and religion to all".
It also said the Algerian government should "refrain from obstructing the religion of persons who do not observe the official religion, in particular by the means of destruction and closure of establishments or refusal to grant registration of religious movements".
A total of six churches have been closed since November 2017 in the North African country. While three were later reopened - as well as a Christian bookshop and day-care centre for Christian children, dozens of churches have also received notifications ordering them to close.
The keyhole of a closed down church sealed with wax in Oran
A new report by the World Evangelical Alliance submitted to the UNHRC in June, stated that the church closures were justified according to a 2006 ordinance, which states permission must be obtained before using a building for non-Muslim worship.
However, World Watch Monitor reports that authorities have failed to respond to almost all applications from churches for places of worship.
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