Kadyrov replaces Sergei Abramov, under whom he had served as deputy premier.
Chechen President Alu Alkhanov said Abramov, who was badly injured in a car accident earlier this winter, had resigned due to health concerns.
The new premier is the son of Akhmad Kadyrov, the Kremlin-backed Chechen president who was assassinated in 2004.
Ramzan Kadyrov also heads a shadowy security force widely alleged to commit abductions and abuse of civilians.
In other developments, three Russian soldiers have reportedly died in a clash with Chechen separatists when they stumbled upon the rebels' forest camp in the Kurchaloi region, east of the capital, Grozny.