The two Russians are on remand, a local interior ministry official told the Qatar News Agency. The Prosecutor General's Office is investigating into the assassination.
The suspects were arrested on February 19, while charges against them were brought on February 25, according to the interior ministry official, who denied the arrestees' names.
The As-Sharq al-Ausat newspaper reported earlier that the suspects had been detained at Dubai airport and escorted to the Qatar authorities. However, Russian acting Foreign Minister Igor Ivanov said in a statement that they had been arrested in Qatar.
Mr Yandarbiyev's car was blown up in downtown Doha last Friday. The Chechen warlord's son-in-law and chauffeur died on the scene, while Mr Yandarbiyev himself died of wounds in hospital. His son Daud is still in hospital.
Mr Ivanov demanded that the Russian nationals be released from illegal custody immediately and allowed to return to Russia.
Mr Ivanov said Russia was not linked to the incident. "The Qatar authorities' attempts to accuse the Russian citizens of the assassination of Yandarbiyev are utterly ungrounded, they are not linked to the incident. The Qatar authorities' insinuations can only be treated as an act of provocation," reads the foreign minister's statement.