Amnesty and Sing for Democracy said in a joint letter that it wanted to draw the singers' attention to human rights and freedom of speech issues in Azerbaijan.
"Both singers should be aware of the situation in the country post-Eurovision," the letter said, referring to the singing contest in the Azeri capital of Baku in May, which spurred protests and rallies by Azeris demanding democracy.
Authorities in Baku arrested dozens of protesters in May and have since arrested several journalists and political activists.
"We Found Love" singer Rihanna, 24, is scheduled to perform in Baku on Saturday. "Hips Don't Lie" singer Shakira, 35, is performing in Baku for football organization FIFA's under 17 women's world cup on October 13, and at another venue in the capital on October 14.
International rights groups often have criticized Azerbaijan for curbing public dissent, while the government in Baku says Azerbaijanis enjoy full freedom of speech.
"Amnesty International believes that the Azerbaijani government should afford all artists, journalists, activists and ordinary citizens the right to express themselves freely without fear of reprisal. We hope that you share our belief," said the letter to Rihanna and Shakira.
Representatives for both singers did not immediately return calls for comment.
(Reporting By Piya Sinha-Roy, editing by Jill Serjeant)
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