The suspected suicide car bomb went off as theatre-goers attended a performance of Shakespeare's Twelfth Night at the Doha Players theatre outside Qatar's capital, Doha, on Saturday night.
The bomb set off a fire that partially destroyed the theatre building and damaged several cars.
One Briton was killed and a number of other people injured, leaving the expatriate community shocked.
It was the first attack of its kind in Qatar, which hosts the US military's Central Command.
The attack came on the second anniversary of the start of the US-led invasion of Iraq.
The blast shattered windows in nearby homes. Western embassies had ranked the risk of terrorist attacks in Qatar as high.