A car exploded about 9:15pm on Saturday night next to a theatre near a British school in the Qatari capital, Aljazeera said, quoting the ministry.
The car was registered in the name of an Egyptian national who has not been heard of since he left his home on Saturday morning, the channel said.
The explosion came on the eve of the second anniversary of the US-led invasion of Iraq.
Reuters, quoting a member of the Qatari investigation team, said the attack was carried out by a suicide bomber. A second Qatari source confirmed this, the news agency said, saying: "There are two dead, including the suicide bomber."
It quoted the investigating team member as saying that a medium-sized vehicle had slammed into the one-storey building housing the theatre, home to The Doha Players.
The British Foreign Office in London said one of the dead was British, but added that the nationality of the wounded was not known.
Brigadier General Ahmad al-Hayki of the Interior Ministry told Aljazeera that the blast had struck the theatre cafeteria and that most of the wounded were Qataris, other Arabs and Asians.
Asked if the blast had any links to attacks in Saudi Arabia and Kuwait, Hayki said: "We do not want to precede events. We have started gathering evidence."
Anti-US sentiment has been high in the region over the Iraq war and US support for Israel.
On Thursday, the purported head of al-Qaida in Saudi Arabia released an audiotape on a website urging attacks on American targets in Qatar, Bahrain, Oman, the United Arab Emirates and the countries neighbouring Iraq.
An Aljazeera correspondent on the scene said about 100 people had been inside the Doha Players theatre, where William Shakespeare's Twelfth Night had been showing.
A fire broke out in the building and the blast set ablaze and damaged cars in the area.
An AFP correspondent about 500m from the scene saw plumes of smoke rising from the site and a large number of ambulances. The blast was heard several kilometres away across the city.
The blast set a portion of the
theatre and some cars ablaze
Police have sealed off the Farij Kalib district, a residential area 5km north of the city centre, where the theatre is located, witnesses said.
US Army Captain Eric Clark said he spoke to a woman who was performing in Shakespeare's Twelfth Night when the blast shook the hall at about 9:15pm (1815 GMT).
"She heard a massive explosion and there was mass chaos and people just exited the building," Clark said by telephone.
A security guard at the nearby Doha English Speaking School said the blast shattered several windows in the school, which was closed at the time, and that a ceiling collapsed in an auditorium.
He said around 40 teachers who lived in the school compound
were evacuated but that none of them was hurt.
While neighbouring Saudi Arabia and Kuwait have seen many attacks in recent months, Qatar, a key US ally, has had no such violence.
Qatar hosts the US military's Central Command.
In February 2004, former Chechen president Salim Khan Yandarbiyev was assassinated in a car bomb blast in Doha, where he had been living in exile for three years.