At least 46 others have been reported wounded by Sunday’s blast.
The commander of Russian forces in the region, Valery Baranov, was among the injured, although earlier reports suggested he was killed.
He underwent emergency surgery at a military hospital to amputate a wounded leg.
Reuters journalist, Adlan Khasanov, was killed in the explosion.
The bomb was apparently concealed in the stadium's structure at annual celebrations marking Moscow's 1945 victory over Nazi Germany.
"Kadyrov passed away on 9 May on the day of our national holiday," Russian President Vladimir Putin was quoted by the Kremlin as saying after meeting the official's son, Ramzan.
Scenes of chaos
There were scenes of pandemonium at the Dinamo stadium after the blast, with people running around in panic and smoke rising from the wreckage of the stands.
Akhmad Kadyrov (R) was seen as
a traitor by Chechen rebels
Television images showed a man carrying a young boy, unconscious and bleeding from the mouth, down the terraces. Another old man, blood pouring through a bandage on his head, was being helped away by two men.
"The bomb was placed inside a concrete part of the stadium," said Khamid Kadayev, Chechnya's deputy interior minister, speaking on television from the scene of the blast.
He said that was why the bomb had not been detected the previous night or on Sunday morning when the stadium was swept by security officials before the Victory Day celebrations.
Television reports suggested the bomb might have been planted in the stadium during reconstruction work over the past three months.
The blast appeared to target the VIP area of the stadium.
Itar-Tass news agency quoted an interior ministry spokesman as saying five people had been detained in connection with the attack. It gave no further details.
Kadyrov, bearded and thick-set, once called on Chechnya's Muslims to fight against the Russian army, but he later made his peace with Moscow and is now viewed by many Chechens as a traitor.
Putin, who has several times declared the war in Chechnya to be effectively over, has made his hardline policy in the region a key part of his domestic policy. He told second world war veterans after the attack:
"There can be no doubt that retribution is unavoidable for those whom we are fighting today. It will be unavoidable for terrorists."
The event marked Russia's
victory in the second world war
The attack on the stadium – a high-security event celebrating a major occasion in Russian history – dealt an enormous blow to Putin's efforts to restore Russian rule in the north Caucasus region.
Kadyrov had been a crucial figure in Putin's attempts to re-establish Russian hegemony in Chechnya. He was elected last October, virtually unchallenged, to build an administration capable of establishing full Russian authority.
Many Chechens, however, boycotted last year’s election, viewing it as a charade.
Acting president named
Interfax news agency said Sergei Abramov, at present Chechen prime minister, would take over as acting president.
The bombing appears to be the boldest attack launched by Chechen rebels on Russian forces since Russian troops reoccupied the area in 1999.
Victory Day is a major national celebration in Russia and of enormous symbolic importance in the country.
Russia has been fighting separatists in the mainly Muslim northern Caucasus region of Chechnya since it first tried to break away in the 1990s.
Moscow re-imposed its rule in the capital Grozny in a 1999 invasion ordered by Putin, but resistance continues.