An Interior Ministry statement, carried on the state news agency QNA, said on Friday that the car had been rigged with explosives at the house before an Egyptian man rammed it into the theatre, popular with Westerners, in the capital, Doha.
It gave no further details on the investigation into the attack in the energy-rich country that is host to the US central command that directed the 2003 invasion of Iraq.
A source close to the investigation told Reuters that the attack was "sophisticated" and authorities were investigating whether the bomber acted alone. A government official has said it is too early to tell whether al-Qaida was involved.
Meanwhile, the US embassy in Doha has urged its citizens to be vigilant and avoid public gatherings during the Easter holiday after an unknown group claimed responsibility for the bombing and vowed to hit churches and "crusader" military bases in the region.
"The recent attack on our consulate in the Saudi city of Jedda and now the suicide bombing here in Doha highlighted the capability and motivation of radical militant groups," the embassy said in a message dated Thursday.
"Attacks could be indiscriminate and against Western, including British, interests"
The British mission said there was a "high threat of terrorism" in Qatar and advised its citizens to take security precautions. "Attacks could be indiscriminate and against Western, including British, interests."
Qatar has boosted security around Western residential compounds and schools, some of which remained shut, after the bombing, which wounded 16 people, mostly Arabs and Asians.
The attack came two days after the suspected al-Qaida leader in Saudi Arabia urged his followers in Qatar and other Gulf states to wage holy war against "crusaders" in the region.
Al-Qaida members have staged attacks in Kuwait and Saudi Arabia, where they targeted the US consulate in Jedda three months ago, killing five locally employed staff.