Witnesses say the bomb was hidden in a package left on the street in the centre of the city near the Shrine of Abbas, a revered Shia imam.
The attack on Sunday is the latest on Iraq's Shia since the US-led invasion of Iraq ousted Saddam Hussein in April last year, and came on the same day as a suicide truck bombing on the occupation headquarters in Baghdad that killed at least 25.
"Around 10 pm (1900 GMT), an explosion shook al-Abbas street, just 100 metres (yards) from the shrine," said 30-year-old witness Ibrahim Turki.
Local health department director Dr Salah Hasnawi said 13 people were admitted to Karbala hospital, one of whom was seriously hurt.
A Shia mosque in Baquba, west of Baghdad, was largely destroyed by a bomb attack on 9 January and left five dead and dozens wounded.
Last month 19 people were killed, including five Bulgarian soldiers and two Thai nationals, when suicide bombers targeted occupation force bases in Karbala.