Representatives of the human rights group have written letters to the stars sharing information about recent violence, protests and violations in Azerbaijan ahead of the singers' upcoming shows in Baku.
The letter, obtained by Reuters, reads: "Both singers should be aware of the situation in the country.
"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."
Rihanna is scheduled to perform in Baku on Saturday, while pregnant Shakira is set for back-to-back dates in the city next week.