Interior ministry officials of the Gulf state on Thursday said the two were suspected to have participated in the killing of Yandarbiyev.
"Two people suspected of participating in the attack were arrested in the context of an investigation carried out by competent authorities into the murder," an official said.
The official gave no further details.
Yandarbiyev, 51, who was residing in Qatar for the past three years was killed and his 13-year-old son wounded when a blast targeted their car as they returned from weekly prayers at a mosque in capital Doha.
Within days of the killing, Qatar's Amir Hamad bin Khalifa al-Thani approved an anti-terrorism law. Officials said Qatar's consultative Shura Council had already been discussing the law, which stipulates death for "terrorist" acts.
The blast was unprecedented in an otherwise tranquil Qatar, which prides itself for safety and security.
The London-based pan-Arab daily Asharq al-Awsat said this week that authorities in Dubai, in neighbouring United Arab Emirates, had handed over two suspects to Qatari authorities who had left Qatar after the blast.
Qatari and UAE officials declined to confirm the report.
Russia considered Yandarbiyev a "terrorist" and had demanded his extradition.
Pro-Moscow Chechens suggested Yandarbiyev's death was linked to internal disputes, while some Chechen rebels blamed Russia.
But Moscow has denied accusations that it was involved in the assassination of the Chechen leader.
Yandarbiyev was added at Russian request last year to a UN list of groups and people with suspected al-Qaida ties.