The rapper performed at the wedding of Nursultan Nazarbayev's grandson last Saturday. The human rights group compared the appearance to a similar visit earlier this summer by Jennifer Lopez to Turkmenistan, another country with a history of human rights violations.
HRF President Thor Halvorssen says in a statement that Kazakhstan is a "human rights wasteland" where entertainers like West would be imprisoned for expressing their views.
West's publicist did not immediately respond to an email seeking comment.
The foundation says Nazarbayev curbs the political rights of his people, suppresses the media and kidnaps the family members of dissidents to maintain his rule.