An interior ministry source told the official QNA news agency that Yandarbiyev, who was residing in Qatar "temporarily," was killed and his 13-year-old son wounded when a bomb blast targeted their car as they returned from weekly prayers at a Doha mosque.
The source said authorities had launched an investigation into the fatal attack.
A source at Al-Hamad hospital, where Yandarbiyev succumbed to serious injuries sustained in the blast, said his son, Daoud, was in stable condition.
Qatar's Al-Jazeera news channel earlier said two bodyguards were killed in the attack. But the hospital official said there were no dead bodyguards and the interior ministry statement made no mention of bodyguards.
A witness said the blast occurred in the Al-Dafna residential area at 1:00 pm (1000 GMT) and the ex-Chechen leader's four-wheel drive vehicle was burned by the explosion.
Russia had demanded Yandarbiyev's extradition from Qatar. Al-Jazeera's correspondent in Moscow quoted a Russian foreign ministry spokesman as saying after news that he was wounded in an attack that Russia insisted on the request for Doha to hand over the former leader of the rebel republic.
Russia accused Yandarbiyev of involvement in the seizure of more than 800 hostages by Chechen rebels at a theater in Moscow in October 2002. A total of 129 hostages died, most of them during a police raid to secure their release, as did all 41 Chechen rebels.
Yandarbiyev was interim president after Dzhokhar Dudayev, a former Soviet air force general who launched the Chechen independence movement after the fall of the Soviet Union, was killed by Russian forces in 1996.
He was replaced by Aslan Maskhadov, who was elected Chechen president in 1997.