Alkhanov, a former interior minister, was plucked from obscurity to head Chechnya in 2004 after a bomb killed Kadyrov's father, Akhmad.
"Building a personality cult and idealising one person will bring no good to our republic and society"
Alu Alkhanov, outgoing Chechen president
Russia has fought two wars against Chechen fighters since 1994 in which thousands of soldiers, activists and civilians have died.
Fighting eased in 2001, but activists and Russian soldiers continue to clash.
The fighting has destroyed much of Chechnya, particularly the capital Grozny, but Kadyrov has led a largely federally-funded campaign to rebuild.
Kadyrov, 30, heads a private guard that has been widely criticised for human rights abuses since Moscow launched an assault to rein in separatists in 1999.
He is said to have has also created a cult of personality, including banners that praise him draping from buildings, a practice which Alkhanov strongly criticised this week.
"Building a personality cult and idealising one person will bring no good to our republic and society," he said.
Putin also appointed Sergei Ivanov, Russia's defence minister, to the post of first deputy prime minister, creating speculation about Russia's presidential succession.
|Kadyrov becomes acting-president |
pending a provincial assembly decision [AFP]
Putin told a cabinet meeting that Ivanov's status was being "raised to the level of first deputy prime minister ... which of course means that in this situation he can't fulfil the role of [defence] minister".
The president said he was "broadening" Ivanov's responsibilities so that he would oversee not only Russia's military-industrial sector but also part of the civilian economy.
The move means Ivanov, 54, is promoted to the same level as another man considered by analysts as a possible successor to Putin, Dmitry Medvedev, first deputy prime minister, and chairman of energy giant Gazprom.