In a fresh report, the UN human rights agency said it had documented "grave human rights violations, such as arbitrary arrests and detentions, enforced disappearances, ill-treatment and torture, and at least one extra-judicial execution."
Moscow annexed the Black Sea peninsula from Ukraine in March 2014 soon after the overthrow of Ukraine's pro-Russian president Viktor Yanukovych following mass protests in Kiev.
Many Western countries have imposed sanctions on Russia to punish it for the annexation.
In Monday's report, the UN Office of the High Commissioner for Human Rights called on Moscow to respect its obligations as an occupying power, demanding that it investigate all cases of alleged torture, abductions and killings involving members of the Russian security forces and Crimean self-defence.
"There is an urgent need for accountability for human rights violations and abuses and for providing the victims with redress," UN rights chief Zeid Ra'ad Al Hussein said in a statement.
Hundreds of prisoners have been illegally transferred from Crimea to Russian prisons, according to the report, which added that at least three detainees had died after not receiving adequate medical care in custody.
The report further condemned Moscow's decision to substitute Ukrainian laws with Russian ones, and also to force people to take Russian citizenship.
Civil servants have had to renounce Ukrainian citizenship or be sacked, while Crimea residents who do not legally qualify as Russians have in effect become foreigners in their home area, the rights office said.
Such people "cannot own agricultural land, vote and be elected, register a religious community, apply to hold a public meeting, hold positions in the public administration" or even register their car, the UN probe found.
"Education in the Ukrainian language has almost disappeared from Crimea," it added.
The rights investigators were not permitted to enter Crimea, so their report is based on interviews conducted from mainland Ukraine.
Kiev also accuses Moscow of backing the pro-Russian insurgency in Ukraine's industrial east in a conflict that has claimed more than 10,000 lives since April 2014.
