Tamim also rejected Russian media reports that said Yamadayev had survived the attack.
"He was shot and died instantly on the scene."
Yamadayev was a Chechen rebel who switched allegiances in the Chechen conflict and became a decorated Russian officer.
A longtime rival of Ramzan Kadyrov, Chechnya's Moscow-backed leader, Yamadayev had challenged Kadyrov for control of Chechen security forces.
"We hope that law enforcement agencies will find the killer," Ali Karimov, a spokesman for President Kadyrov in the Chechen capital, Grozny, said.
Karimov did not elaborate on the incident.
Yamadayev left Russia after his brother, Ruslan, was shot and killed in central Moscow last September.
Russia has waged a brutal war against Chechen separatists since the 1990s.
The violence began when a former Soviet air force officer seized power and declared independence after the collapse of the Soviet Union.
Russia eventually allowed former rebels who switched sides to take over the local Chechen government.