Chechen guerrillas opposing Moscow's rule are blamed for Sunday's bombing in the capital Grozny, which killed at least seven people.
Putin announced his visit to Chechnya after returning to Moscow, paying tribute to Kadyrov in a cabinet meeting.
"He was, of course, a unique man -- a man of absolute integrity, decency and utmost courage," Putin said of the former separatist-leader-turned-president.
"He never asked for anything for himself. Whenever we met and whatever we talked about, it was always about the interests of the Chechen people. And of course, a people that has such sons cannot but deserve respect."
The assassination may derail Putin's plans for Chechnya, where he had hoped Kadyrov would be able to pacify the war-torn region. Putin had repeatedly said that the situation in Chechnya is rapidly returning to normal, although killings continue to occur on a regular basis in the province.
Russia's chief election commissioner announced that presidential elections to replace the slain Kadyrov will be held by the beginning of September. In the meantime, 32-year-old Prime Minister Sergei Abramov has been named acting president.
Kadyrov's son, Ramzan, will act as deputy head of the government, in a move drawing fire from Chechen separatists. Some accuse Ramzan, who heads a powerful militia called the Kadyrovtsy, of orchestrating torture, murder and kidnappings, which he denies.
There is widespread speculation that Putin is grooming Ramzan to become the next Chechen president. A militant rebel Web site posted a statement saying, "You don't have to be Nostradamus to guess the fate of Ramzan Kadyrov. If he stays alive until the elections, it will be a major success for Moscow."
In the wake of the assassination, Putin ordered at least 1,000 additional troops be added to the Chechen Interior Ministry's forces, according to Russian news agency Itar-Tass.
"The Interior Ministry of Chechnya asked for a speedy decision on the question of raising the staff strength by 1,125 people," the news agency quoted the president as saying.
"The acting Russian interior minister and the prime minister must consider this question and quickly resolve it. ... By the end of the day report to me."
Russian currently has around 70,000 troops and police in Chechnya.
Putin also announced his intent to send an economic team to assess possibilities for rebuilding the province, the site of a decade-long war between separatists and Moscow.
"We need to look again at the reconstruction of Grozny. Despite all that is being done there, it looks horrible from a helicopter," Putin said of the Chechen capital city.
Russia has been fighting Chechen rebels since the republic first attempted to break from Moscow's rule in the 1990s.