"[The blast] could be revenge by extremists for the destruction of the leaders of bandit groups and could be aimed at destabilising the situation in the republic during May holidays," the Itar-Tass news agency quoted Kanokov as saying.
Interfax said the victim, who died in hospital, was a 104-year-old veteran of the second world war.
'Designed to injure'
The bomb was equipped with a timer and filled with pieces of metal designed to injure as many people as possible, Marina Kyasova, a spokesman for the regional interior ministry, told the Reuters news agency.
"At least 21 people were injured but the exact number is still being defined," she said.
There was no immediate claim of responsibility for the attack.
Dmitry Medvedev, the Russian president, has ordered a federal probe into the incident.
The attack drew comparisons with the blast that killed Akhmat Kadyrov, the former president of Chechnya and the father of current president Ramzan Kadyrov, at a football stadium in 2004.
Kabardino-Balkaria has mostly avoided the large-scale violence of nearby Chechnya, Ingushetia or Dagestan, but attacks have spiked in recent months.
On Friday, four people including two police officers were injured in a bomb blast in
In the neighbouring republic of Ingushetia, a man was shot dead by policemen after opening fire at a sports complex on Saturday, an interior ministry spokeswoman said.
The man opened fire after policemen began to search him at the entrance to the sports complex in the city of Nazran, where the Yunus-Bek Yevkurov, the Ingush president, and other officials were attending a national judo competition.
In 2009 alone, more than 1,000 Russian security personnel and separatist fighters died in confrontations across the North Caucasus.